power - how many times to use the number in a multiplication

-3x to the negative one power

-3x to the negative one power
Raising to a negative power means taking 1 over the same expression to the positive power"
(-3x)^-1 = 1/-3x = [B]-1/3x[/B]

-x squared

-x squared
We take -x and raise it to the 2nd power:
(-x)^2 = -x * -x = [B]x^2[/B]

1 multiplied by b squared multiplied by c squared

1 multiplied by b squared multiplied by c squared
b squared means we raise b to the power of 2:
b^2
c squared means we raise c to the power of 2:
c^2
b squared multiplied by c squared
b^2c^2
1 multiplied by b squared multiplied by c squared means we multiply 1 by b^2c^2
1b^2c^2
Multiplying by 1 can be written by [U][I]removing[/I][/U] the 1 since it's an identity multiplication:
[B]b^2c^2[/B]

1 over 14 cubed

1 over 14 cubed
14 cubed means we raise 14 to the power of 3:
14^3
1 over 14 cubed is written as:
1/14^3
To simplify this, we [URL='https://www.mathcelebrity.com/powersq.php?sqconst=+6&num=14%5E3&pl=Calculate']evaluate 14^3[/URL] = 2744
So we have:
[B]1/2744[/B]

10, 1,000, 100,000, 10,000,000 What power of 10 is the 80th term?

10, 1,000, 100,000, 10,000,000
What power of 10 is the 80th term?
We see the following pattern
10^1 = 10
10^3 = 1000
10^5 = 100,000
10^7 = 10,000,000
f(n) = 10^(2n - 1)
We build the 80th term:
f(80) = 10^(2(80) - 1)
f(80) = 10^(160 - 1)
f(80) = 10^[B]159[/B]

11 to the power of 6 multiply 11 to the power of 3

11 to the power of 6 multiply 11 to the power of 3
Take this in parts.
[U]Step 1: 11 to the power of 6 means we raise 11 to the 6th power using exponents:[/U]
11^6
[U]Step 2: 11 to the power of 3 means we raise 11 to the 3rd power using exponents:[/U]
11^3
[U]Step 3: Multiply each term together:[/U]
11^6 * 11^3
[U]Step 4: Simplify[/U]
Because we have 2 numbers that are the same, in this case, 11, we can add the exponents together when multiplying:
11^(6 + 3)
[B]11^9
[MEDIA=youtube]gCxVq7LqyHk[/MEDIA][/B]

15 less than a number squared

15 less than a number squared
A number is denoted by an arbitrary variable, let's call it x.
x
Squared means we raise that number to a power of 2
x^2
15 less means we subtract
[B]x^2 -15[/B]

2 times b squared minus 6

2 times b squared minus 6
b squared means we raise b to the 2nd power:
b^2
2 times b squared
2b^2
Minus 6:
[B]2b^2 - 6[/B]

2/5 the cube of a number

2/5 the cube of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The cube of a number means we raise x to the power of 3:
x^3
2/5 of the cube means we multiply x^3 by 2/5:
[B](2x^3)/5[/B]

2x plus 8, quantity squared

2x plus 8, quantity squared
2x plus 8 means we add 8 to 2x:
2x + 8
Squaring the quantity means we raise it to the power of 2:
[B](2x + 8)^2[/B]

3 is subtracted from square of a number

3 is subtracted from square of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Square of a number means we raise x to the 2nd power:
x^2
3 is subtracted from square of a number
[B]x^2 - 3[/B]

3 is subtracted from the square of x

3 is subtracted from the square of x
Let's take this algebraic expression in two parts:
Part 1: The square of x means we raise x to the power of 2:
x^2
Part 2: 3 is subtracted means we subtract 3 from x^2
[B]x^2 - 3[/B]

3 to the power of 2 times 3 to the power of x equals 3 to the power of 7

3 to the power of 2 times 3 to the power of x equals 3 to the power of 7.
Write this out:
3^2 * 3^x = 3^7
When we multiply matching coefficients, we add exponents, so we have:
3^(2 + x) = 3^7
Therefore, 2 + x = 7. To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=2%2Bx%3D7&pl=Solve']type it into our search engine[/URL] and we get:
x = [B]5[/B]

30 increased by 3 times the square of a number

30 increased by 3 times the square of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x
x
The square of a number means we raise x to the power of 2:
x^2
3 times the square:
3x^2
The phrase [I]increased by[/I] means we add 3x^2 to 30:
[B]30 + 3x^2[/B]

3abc^4/12a^3(b^3c^2)^2 * 8ab^-4c/4a^2b

3abc^4/12a^3(b^3c^2)^2 * 8ab^-4c/4a^2b
Expand term 1:
3abc^4/12a^3(b^3c^2)^2
3abc^4/12a^3b^6c^4
Now simplify term 1:
3/12 = 1/4
c^4 terms cancel
Subtract powers from variables since the denominator powers are higher:
b^(6 - 1) = b^5
a^(3 - 1) = a^2
1/4a^2b^5
Now simplify term 2:
8ab^-4c/4a^2b
8/4 = 2
2c/a^(2 - 1)b^(1 - -4)
2c/ab^5
Now multiply simplified term 1 times simplified term 2:
1/4a^2b^5 * 2c/ab^5
(1 * 2c)/(4a^2b^5 * ab^5)
2c/4a^(2 + 1)b^(5 + 5)
2c/4a^3b^10
2/4 = 1/2, so we have:
[B]c/2a^3b^10[/B]

3x to the power 2n

3x to the power 2n
We take the expression 3x raise it to the power of 2n
[B](3x)^2n[/B]

4 multiplied by the cube of p is reduced by 5

4 multiplied by the cube of p is reduced by 5
The cube of p means we raise p to the 3rd power:
p^3
4 multiplied by the cube of p
4p^3
reduced by 5:
[B]4p^3 - 5[/B]

4 times 8 to the sixth power

4 times 8 to the sixth power
8 to the 6th power:
8^6
4 times this amount:
4 * 8^6
To evaluate this expression, we [URL='https://www.mathcelebrity.com/order-of-operations-calculator.php?num=4%2A8%5E6&pl=Perform+Order+of+Operations']type it in our search engine[/URL] and we get:
1,048,576

4 times a number cubed decreased by 7

4 times a number cubed decreased by 7
A number is denoted as an arbitrary variable, let's call it x
x
Cubed means raise x to the third power
x^3
Decreased by 7 means subtract 7
x^3 - 7

4 times of the sum of the cubes of x and y

4 times of the sum of the cubes of x and y
The cube of x means we raise x to the 3rd power:
x^3
The cube of y means we raise y to the 3rd power:
y^3
The sum of the cubes means we add:
x^3 + y^3
4 times the sum of the cubes:
[B]4(x^3 + y^3)[/B]

4 times the sum of 3 plus x squared

4 times the sum of 3 plus x squared
x squared means we raise x to the power of 2:
x^2
3 plus x squared:
3 + x^2
4 times the sum of 3 plus x squared
3(3 + x^2)

5 more than twice the cube of a number

5 more than twice the cube of a number.
Take this algebraic expression in pieces.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The cube of a number means we raise it to a power of 3
x^3
Twice the cube of a number means we multiply x^3 by 2
2x^3
5 more than twice the cube of a number means we multiply 2x^3 by 5
5(2x^3)
Simplifying, we get:
10x^3

5 more than twice the cube of a number

5 more than twice the cube of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
The cube of a number means we raise x to the power of 3:
x^3
Twice the cube means we multiply x^3 by 2
2x^3
Finally, 5 more than twice the cube means we add 5 to 2x^3:
[B]2x^3 + 5[/B]

5 times g reduced by the square of h

5 times g reduced by the square of h
Take this algebraic expression in pieces:
[LIST=1]
[*]5 times g means we multiply g by 5: 5g
[*]The square of h means we raise h to the 2nd power: h^2
[*]5 times g reduced by the square of h means we subtract h^2 from 5g:
[/LIST]
[B]5g - h^2[/B]

6 is divided by square of a number

6 is divided by square of a number
The phrase [I]a number [/I]means an arbitrary variable, let's call it x.
x
the square of this means we raise x to the power of 2:
x^2
Next, we divide 6 by x^2:
[B]6/x^2[/B]

6 times j squared minus twice j squared

6 times j squared minus twice j squared
j squared means we raise the variable j to the power of 2:
j^2
6 times j squared means we multiply j^2 by 6:
6j^2
Twice j squared means we multiply j^2 by 2:
2j^2
The word [I]minus[/I] means we subtract 2j^2 from 6j^2
6j^2 - 2j^2
So if you must simplify, we group like terms and get:
(6 - 2)j^2
[B]4j^2[/B]

6 times y divided by x squared

6 times y divided by x squared
6 times y:
6y
x squared means we raise x to the power of 2:
x^2
The phrase [I]divided by[/I] means we have a fraction:
[B]6y/x^2[/B]

6 times y divided by x squared

6 times y divided by x squared
6 times y:
6y
x squared means we raise x to the power of 2:
x^2
The phrase [I]divided by[/I] means we divide 6y by x^2:
[B]6y/x^2[/B]

64 divided by the cube of y

64 divided by the cube of y
The cube of y means y raised to the 3rd power:
y^3
64 divided by this:
[B]64/y^3[/B]

7 subtracted from x cubed

7 subtracted from x cubed
x cubed means x raised to the 3rd power
x^3
7 subtracted from this
[B]x^3 - 7[/B]

7 times the cube of the sum of x and 8

7 times the cube of the sum of x and 8
Take this algebraic expression in 3 parts:
[LIST=1]
[*]The sum of x and 8 means we add 8 to x: x + 8
[*]The cube of this sum means we raise the sum to the 3rd power: (x + 8)^3
[*]7 times this cubed sum means we multiply (x + 8)^3 by 7:
[/LIST]
[B]7(x + 8)^3[/B]

8 is subtracted from the square of x

8 is subtracted from the square of x
Take this algebraic expression in parts:
[LIST]
[*]The square of x means we raise x to the power of 2: x^2
[*]8 subtracted from the square of x is found by subtracting 8 from x^2
[/LIST]
[B]x^2 - 8[/B]

8 times 4 plus m squared

8 times 4 plus m squared
m squared means we raise m to the power of 2
m^2
4 plus m squared:
4 + m^2
8 times 4 plus m squared
[B]8(4 + m^2)[/B]

8 to the power of 8 divided by 8

8 to the power of 8 divided by 8
8 to the power of 8
8^8
Divided by 8
[B]8^8/8[/B]

8 to the power of x over 2 to the power of y

8 to the power of x over 2 to the power of y
Step 1: 8 to the power of x means we take 8 and raise it to an exponent of x:
8^x
Step 2: 2 to the power of y means we take 2 and raise it to an exponent of y:
2^y
Step 3: The word [I]over[/I] means a quotient, also known as divided by, so we have:
[B]8^x/2^y
[MEDIA=youtube]SPQKOt5EoqA[/MEDIA][/B]

A car drives 3 feet the first second, 9 feet in the next second, and 27 feet in the third second. If

A car drives 3 feet the first second, 9 feet in the next second, and 27 feet in the third second. If the pattern stays the same, how far will the car have traveled after 5 seconds, in feet?
Our pattern is found by the distance function D(t), where we have 3 to the power of the time (t) in seconds as seen below:
D(t) = 3^t
The problem asks for D(5):
D(5) = 3^5
[URL='https://www.mathcelebrity.com/powersq.php?sqconst=+6&num=3%5E5&pl=Calculate']D(5)[/URL] = [B]243[/B]

A cupe-shaped tank has edge lengths of 1/2 foot. Sheldon used the expression s to the power of 3 = v

A cupe-shaped tank has edge lengths of 1/2 foot. Sheldon used the expression s to the power of 3 = v to find the volume. What was the volume of the tank?
1/2 foot = 6 inches
v = (6)^3
v = [B]216 cubic inches[/B]

A Septon said that he has a collection of 1,000,000 stones in his house. How many stones is that in

A Septon said that he has a collection of 1,000,000 stones in his house. How many stones is that in base 10?
The 1 is in decimal position 7, or 6th power.
[URL='https://www.mathcelebrity.com/powersq.php?sqconst=+6&num=7%5E6&pl=Calculate']1 * 7^6[/URL] = [B]117,649[/B]

A square of an integer is the integer. Find the integer.

A square of an integer is the integer. Find the integer.
Let the integer be n. The square means we raise n to the power of 2, so we have:
n^2 = n
Subtract n from each side:
n^2 - n = n - n
n^2 - n = 0
Factoring this, we get:
n(n - 1) = 0
So n is either [B]0 or 1[/B].

A times r squared multiplied by h

A times r squared multiplied by h
r squared means we raise r to the power of 2:
r^2
a times r squared:
ar^2
Multiplied by h:
[B]ahr^2[/B]

add 7 and 2, raise the result to the 6th power, then add what you have to s

add 7 and 2, raise the result to the 6th power, then add what you have to s
Add 7 and 2:
7 + 2
Simplify this, we get:9
Raise the result to the 6th power:
9^6
[URL='https://www.mathcelebrity.com/powersq.php?sqconst=+6&num=9%5E6&pl=Calculate']Simplifying this using our exponent calculator[/URL], we get:
531,441
Now, we add what we have (our result) to s to get our final algebraic expression:
[B]s + 531,441[/B]

add d to 5, raise the result to the 9th power, then subtract what you have from 2

add d to 5, raise the result to the 9th power, then subtract what you have from 2
Add d to 5:
d + 5
Raise the result to the 9th power means we raise (d + 5) to the 9th power using an exponent:
(d + 5)^9
the subtract what we have (the result) from 2:
[B]2 - (d + 5)^9[/B]

As the sample size increases, we assume:

As the sample size increases, we assume:
a. ? increases
b. ? increases
c. The probability of rejecting a hypothesis increases
d. Power increases
[B]d. Power increases[/B]
[LIST]
[*]Power increases if the standard deviation is smaller.
[*]If the difference between the means is bigger, the power is bigger.
[*]Sample size also increases power
[/LIST]

b to the fifth power decreased by 7

b to the fifth power decreased by 7
Take this algebraic expression in steps:
[LIST]
[*]b to the fifth power: b^5
[*]Decreased by 7 means we subtract 7 from b^5: [B]b^5 - 7[/B]
[/LIST]

Binominal Probability

If a seed is planted, it has a 90% chance of growing into a healthy plant.
If 12 seeds are planted, what is the probability that exactly 4 don't grow?
Im seriously confused is it like u multiple the amount of the (0.90) and multiple (0.30) by power depends how any they r right?

C varies directly as the cube of a and inversely as the 4th power of B

C varies directly as the cube of a and inversely as the 4th power of B
The cube of a means we raise a to the 3rd power:
a^3
The 4th power of B means we raise b to the 4th power:
b^4
Varies directly means there exists a constant k such that:
C = ka^3
Also, varies inversely means we divide by the 4th power of B
C = [B]ka^3/b^4[/B]
Varies [I]directly [/I]as means we multiply by the constant k.
Varies [I]inversely [/I]means we divide k by the term which has inverse variation.
[MEDIA=youtube]fSsG1OB3qdk[/MEDIA]

c varies jointly as the square of q and cube of p

c varies jointly as the square of q and cube of p
The square of q means we raise q to the 2nd power:
q^2
The cube of p means we raise p to the rdd power:
p^3
The phrase [I]varies jointly[/I] means there exists a constant k such that:
[B]c = kp^3q^2[/B]

cube root of a number and 7

cube root of a number and 7
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Cube root of a number means we raise x to the 1/3 power:
x^1/3
And 7 means we add 7:
[B]x^1/3 + 7[/B]

Cube the difference of b and c

Cube the difference of b and c
the difference of b and c:
b - c
Cubing means raising to the power of 3:
[B](b - c)^3[/B]

d squared is greater than or equal to 17

d squared is greater than or equal to 17
d squared means we raise the variable d to the power of 2:
d^2
The phrase [I]greater than or equal to[/I] means an inequality. So we set this up using the >= in relation to 17:
[B]d^2 >= 17[/B]

Derivatives

This lesson walks you through the derivative definition, rules, and examples including the power rule, derivative of a constant, chain rule

Direct Current (Electrical Engineering) Ohms Law

Enter two of the following items from the DIRECT CURRENT(DC) electrical engineering set of variables, and this will solve for the remaining two:

* I = current(amps.)

* V = Electricity potential of voltage(volts)

* R = resistance(ohms)

* P = power(watts)

* I = current(amps.)

* V = Electricity potential of voltage(volts)

* R = resistance(ohms)

* P = power(watts)

divide 8 by t, raise the result to the 7th power

divide 8 by t, raise the result to the 7th power.
We take this algebraic expression in two parts:
1. Divide 8 by t
8/t
2. Raise the result to the 7th power. (This means we use an exponent of 7)
[B](8/t)^7[/B]

Divide the sum of a and b by the square of c

Divide the sum of a and b by the square of c
The sum of a and b:
a + b
The square of c means we raise c to the power of 2:
c^2
Divide means we have a quotient, with a + b on top, and c^2 on the bottom:
[B](a + b)/c^2[/B]

divide the sum of the square of a and b by thrice c

divide the sum of the square of a and b by thrice c
Sum of the squares of a and b is found as follows:
[LIST]
[*]a squared means we raise a to the power of 2: a^2
[*]b squared means we raise b to the power of 2: b^2
[*]Sum of the squares means we add both terms: a^2 + b^2
[*]Thrice c means we multiply c by 3: 3c
[/LIST]
Divide means we have a quotient:
[B](a^2 + b^2)/3c[/B]

Divide x cubed by the quantity x minus 7

Divide x cubed by the quantity x minus 7
x cubed means we raise x to the power of 3:
x^3
We divide this by x - 7:
[B]x^3/(x - 7)[/B]

double 6 , divide the result by y ,then raise what you have to the 10th power

double 6 , divide the result by y ,then raise what you have to the 10th power
Take this in pieces:
Double 6 means multiply 6 by 2 --> 6(2) = 12
Divide the result by y:
12/y
Then raise what you have to the 10th power:
[B](12/y)^10[/B]

double v, raise the result to the 6th power, then multiply what you have by w

double v, raise the result to the 6th power, then multiply what you have by w
Double v means multiply v by 2:
2v
Raise the result to the 6th power, means we use an exponent of 6 on 2v:
(2v)^6
Then multiply what you have by w, means take the result above, and multiply by w:
[B]w(2v)^6[/B]

evaluate 16 raised to 1/4

evaluate 16 raised to 1/4
What number raised to the 4th power equals 16?
[B]2[/B], since 2 * 2 * 2 * 2 = 16

Expand Master and Build Polynomial Equations

This calculator is the __ultimate__ expansion tool to multiply polynomials. It expands algebraic expressions listed below using all 26 variables (a-z) as well as negative powers to handle polynomial multiplication. Includes multiple variable expressions as well as outside multipliers.

Also produces a polynomial equation from a given set of roots (polynomial zeros). * Binomial Expansions c(a + b)^{x}

* Polynomial Expansions c(d + e + f)^{x}

* FOIL Expansions (a + b)(c + d)

* Multiple Parentheses Multiplications c(a + b)(d + e)(f + g)(h + i)

Also produces a polynomial equation from a given set of roots (polynomial zeros). * Binomial Expansions c(a + b)

* Polynomial Expansions c(d + e + f)

* FOIL Expansions (a + b)(c + d)

* Multiple Parentheses Multiplications c(a + b)(d + e)(f + g)(h + i)

Explain the relationship between "squaring" a number and finding the "square root" of a number. Use

Explain the relationship between "squaring" a number and finding the "square root" of a number. Use an example to further explain your answer.
Squaring a number means raising it to the power of 2
The square root of a number [I]undoes[/I] a square of a number.
So square root of x^2 is x
x squared is x^2
Let x = 5.
x squared = 5^2 = 25
Square root of 25 = square root of 5^2 = 5

Factorization

Given a positive integer, this calculates the following for that number:

1) Factor pairs and prime factorization and prime power decomposition

2) Factors and Proper Factors 3) Aliquot Sum

1) Factor pairs and prime factorization and prime power decomposition

2) Factors and Proper Factors 3) Aliquot Sum

Find the subset of {a,b,c,d,e}

Find the subset of {a,b,c,d,e}
Using our power set calculator, we find [URL='https://www.mathcelebrity.com/powerset.php?num=a%2Cb%2Cc%2Cd%2Ce&pl=Show+Power+Set+and+Partitions']all the 32 subsets of {a,b,c,d,e}[/URL]

H minus 6 all cubed

H minus 6 all cubed
H minus 6
h - 6
All cubed means raise the entire expression to the 3rd power
(h - 6)^3

How can you rewrite the number 1 as 2 to a power?

How can you rewrite the number 1 as 2 to a power?
There exists an identity which says, n^0 = 1 where n is a number.
So [B]2^0 = 1[/B]

if a number is added to its square, it equals 20

if a number is added to its square, it equals 20.
Let the number be an arbitrary variable, let's call it n.
The square of the number means we raise n to the power of 2:
n^2
We add n^2 to n:
n^2 + n
It equals 20 so we set n^2 + n equal to 20
n^2 + n = 20
This is a quadratic equation. So [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2%2Bn%3D20&pl=Solve+Quadratic+Equation&hintnum=+0']we type this equation into our search engine[/URL] to solve for n and we get two solutions:
[B]n = (-5, 4)[/B]

If a, b, and c are positive integers such that a^b = x and c^b = y, then xy = ?

If a, b, and c are positive integers such that a^b = x and c^b = y, then xy = ?
A) ac^b
B) ac^2b
C) (ac)^b
D) (ac)^2b
E) (ac)^b^2
xy = a^b * c^b
We can use the Power of a Product Rule
a^b * c^b = (ac)^b
Therefore:
xy = [B](ac)^b - Answer C[/B]

If power is big, you can assume:

If power is big, you can assume:
a. The difference between the means is more likely to be detected
b. The significance level set by the researcher must be high
c. We increase the probability of type I error
d. Your study result will be more likely to be inconclusive
[B]b. The significance level set by the researcher must be high[/B]

If the probability that you will correctly reject a false null hypothesis is 0.80 at 0.05 significan

If the probability that you will correctly reject a false null hypothesis is 0.80 at 0.05 significance level. Therefore, ? is__ and ? is__.
[LIST]
[*]? represents the significance level of 0.05
[*]We want the Power of a Test which is 1 - ? = 0.8 so ? = 0.20
[/LIST]
Our answer is: [B]0.05, 0.20 [/B]

Imaginary Numbers

Calculates the imaginary number i where i = √-1 raised to any integer power as well as the product of imaginary numbers of quotient of imaginary numbers

In a hurricane the wind pressure varies directly as the square of the wind velocity. If a wind pres

In a hurricane the wind pressure varies directly as the square of the wind velocity. If a wind pressure is a measure of a hurricane's destruction capacity, what happens to this destructive power when the wind speed doubles?
Let P = pressure and v = velocity (wind speed)
We are given p = v^2
Double velocity, so we have a new pressure P2:
P2 = (2v)^2
P2 = 4v^2
Compare the 2:
p = v^2
p = 4v^2
Doubling the wind speed [B]quadruples, or 4 times[/B] the pressure.

index form of (5^3)^6

Index form of (5^3)^6
Index form is written as a number raised to a power.
Let's simplify by multiply the exponents. Since 6*3 = 18, We have:
[B]5^18[/B]

Is someone has $1,000,000 in base 2, how much money does she have in base 10?

Is someone has $1,000,000 in base 2, how much money does she have in base 10?
1 is in 7th digit place, so we raise it to the 6th power:
[URL='https://www.mathcelebrity.com/powersq.php?sqconst=+6&num=2%5E6&pl=Calculate']1 * 2^6 [/URL]= [B]64[/B]

Kamille is calculating the length of diagonal on a picture board and gets a solution of the square r

Kamille is calculating the length of diagonal on a picture board and gets a solution of the square root of 58. She needs to buy the ribbon to put across the diagonal of the board, so she estimates that she will need at least 60 inches of ribbon to cover the diagonal. Is she correct? Explain.
[URL='https://www.mathcelebrity.com/powersq.php?num=sqrt%2858%29&pl=Calculate']The square root of 58 [/URL]has an answer between 7 and 8.
So Kamille is [B]incorrect[/B]. She needs much less than 60 inches of ribbon. She needs less than 8 inches of ribbon.

Literal Equations

Solves literal equations with no powers for a variable of your choice as well as open sentences.

Logarithms and Natural Logarithms and Eulers Constant (e)

This calculator does the following:

* Takes the Natural Log base e of a number x Ln(x) → log_{e}x

* Raises e to a power of y, e^{y}

* Performs the change of base rule on log_{b}(x)

* Solves equations in the form b^{cx} = d where b, c, and d are constants and x is any variable a-z

* Solves equations in the form ce^{dx}=b where b, c, and d are constants, e is Eulers Constant = 2.71828182846, and x is any variable a-z

* Exponential form to logarithmic form for expressions such as 5^{3} = 125 to logarithmic form

* Logarithmic form to exponential form for expressions such as Log_{5}125 = 3

* Takes the Natural Log base e of a number x Ln(x) → log

* Raises e to a power of y, e

* Performs the change of base rule on log

* Solves equations in the form b

* Solves equations in the form ce

* Exponential form to logarithmic form for expressions such as 5

* Logarithmic form to exponential form for expressions such as Log

mcubemultipliedbyntothefourthpower

mcubemultipliedbyntothefourthpower
m cubed means we raise m to the 3rd power:
m^3
n to the fourth power:
n^4
Multiply both expressions together:
[B]m^3n^4[/B]

Monomials

This calculator will raise a monomial to a power,multiply monomials, or divide monomials.

Multiply c by five and square the answer

Multiply c by five and square the answer
Multiply c by five:
5c
Square the answer means we raise 5c to the power of 2:
[B](5c)^2 [/B]
This can also be written as [B]25c^2[/B]

N squared multiplied by the difference of n and 3

N squared multiplied by the difference of n and 3
n squared means we raise n to the power of 2:
n^2
The difference of n and 3 means we subtract 3 from n:
n - 3
Now we multiply both terms together:
[B]n^2(n - 3)[/B]

Number Property

This calculator determines if an integer you entered has any of the following properties:

* Even Numbers or Odd Numbers (Parity Function or even-odd numbers)

* Evil Numbers or Odious Numbers

* Perfect Numbers, Abundant Numbers, or Deficient Numbers

* Triangular Numbers

* Prime Numbers or Composite Numbers

* Automorphic (Curious)

* Undulating Numbers

* Square Numbers

* Cube Numbers

* Palindrome Numbers

* Repunit Numbers

* Apocalyptic Power

* Pentagonal

* Tetrahedral (Pyramidal)

* Narcissistic (Plus Perfect)

* Catalan

* Repunit

* Even Numbers or Odd Numbers (Parity Function or even-odd numbers)

* Evil Numbers or Odious Numbers

* Perfect Numbers, Abundant Numbers, or Deficient Numbers

* Triangular Numbers

* Prime Numbers or Composite Numbers

* Automorphic (Curious)

* Undulating Numbers

* Square Numbers

* Cube Numbers

* Palindrome Numbers

* Repunit Numbers

* Apocalyptic Power

* Pentagonal

* Tetrahedral (Pyramidal)

* Narcissistic (Plus Perfect)

* Catalan

* Repunit

One fifth of the square of a number

One fifth of the square of a number
We have an algebraic expression. Let's break this into parts.
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x
[*]The square of a number means we raise it to the power of 2. So we have x^2
[*]One-fifth means we have a fraction, where we divide our x^2 in Step 2 by 5. So we get our final answer below:
[/LIST]
[B]x^2/5[/B]

p more than the square of q

p more than the square of q
Take this algebraic expression in parts:
Step 1: Square of q means raise q to the 2nd power:
q^2
Step 2: The phrase [I]more[/I] means we add p to q^2
[B]q^2 + p[/B]

Please help!!

(1) |P(A)| = 4 <-- Cardinality of the power set is 4, which means we have 2^n = 4.[B] |A| = 2
[/B]
(2) |B| = |A|+ 1 and |A×B| = 30
|B| = 6 if [B]|A| = 5[/B] and |A x B| = 30
(3) |B| = |A|+ 2 and |P(B)|?|P(A)| = 24
Since |B| = |A|+ 2, we have: 2^(a + 2) - 2^a = 24
2^a(2^2 - 1) = 24
2^a(3) = 24
2^a = 8
[B]|A |= 3[/B]
To check, we have |B| = |A| + 2 --> 3 + 2 = 5
So |P(B)| = 2^5 = 32
|P(A)| = 2^3 = 8
And 32 - 8 = 24

Power is equal to:

Power is equal to:
a. ?
b. ?
c. 1 - ?
d. 1 - ?
[B]d. 1 - ?[/B]
[B][/B]
[I]Correct Decision 1 - ? = Power of a Test[/I]

power set for S= {b,c,f}

power set for S= {b,c,f}
The [I]power set[/I] P is the set of all subsets of S including S and the empty set ?.
Since S contains 3 terms, our Power Set should contain 2^3 = 8 items
[URL='https://www.mathcelebrity.com/powerset.php?num=b%2Cc%2Cf&pl=Show+Power+Set+and+Partitions']Link to power set for this problem[/URL]
P = [B]{{}, {b}, {c}, {f}, {b,c}, {b,f}, {c,f}, {b,c,f}}[/B]

Power Sets and Set Partitions

Given a set S, this calculator will determine the power set for S and all the partitions of a set.

Powers Of

Determines the powers of a number from 1 to n.

q to the 10th power subtracted from 100

q to the 10th power subtracted from 100
q to the 10th power:
q^10
We subtract this from 100:
[B]100 - q^10[/B]

r squared plus the product of 3 and s plus 5

r squared plus the product of 3 and s plus 5
r squared means we raise r to the power of 2
r^2
The product of 3 and s means we multiply s by 3:
3s
plus 5 means we add
3s + 5
R squared plus means we add r^2:
[B]r^2 + 3s + 5[/B]

raise 2 to the 10th power and divide k by the result

raise 2 to the 10th power and divide k by the result
Raise 2 to the 10th power:
2^10
Divide k by the result:
k / 2^10

Raise 3 to 9th power then multiply b by the result

Raise 3 to 9th power then multiply b by the result
3^9th power:
3^9
Multiply b by the result?
[B]3^9 * b[/B]

raise 3 to the 4th power, subtract w from the result, then divide v by what you have

raise 3 to the 4th power, subtract w from the result, then divide v by what you have
Raise 3 to the 4th power:
3^4
Simplified, this is
81
Subtract w from the result. We subtract w from 81:
81 - w
Then divide v by what you have. We divide v by (81 -w)
[B]v/(81 - w)[/B]

raise 3 to the 8th power, then divide the result by t

raise 3 to the 8th power, then divide the result by t
3 to the 8th power
3^8
Divide the result by t
3^8/t
Now, if they want you to evaluate 3 to the 8th, you have:
6,561/t

raise 6 to the 4th power, add h to the result, then multiply what you have by 8

raise 6 to the 4th power, add h to the result, then multiply what you have by 8
Raise 6 to the 4th power:
6^4
add h to the result:
6^4 + h
Then multiply what we have by 8:
[B]8(6^4 + h)[/B]

Raise 9 to the 3rd power, subtract d from the result, then divide what you have by c

Raise 9 to the 3rd power, subtract d from the result, then divide what you have by c.
This is an algebraic expression, let's take in parts (or chunks).
Raise 9 to the 3rd power. This means we take 9, and raise it to an exponent of 3
9^3
Subtract d from the result, means we subtract d from 9^3
9^3 - d
Now we divide 9^3 - d by c
[B](9^3 - d) / c[/B]

Raise a to the 4th power then find the sum of the result and b

Raise a to the 4th power then find the sum of the result and b
Raise a to the 4th:
a^4
Then get the sum of this and b
[B]a^4 + b[/B]

raise b to the 6th power then find the sum of the result and 4

raise b to the 6th power then find the sum of the result and 4
raise b to the 6th power
b^6
raise b to the 6th power then find the sum of the result and 4
[B]b^6 + 4[/B]

raise c to the 2nd power, add the result to 8, then subtract what you have from d

raise c to the 2nd power, add the result to 8, then subtract what you have from d
Raise c to the 2nd power:
c^2
Add the result to 8:
c^2 + 8
Subtract what you have from d:
d - (c^2 + 8)

Raise c to the 7th power, divide the result by 4, then triple what you have

Raise c to the 7th power, divide the result by 4, then triple what you have.
Take this algebraic expression in pieces.
Raise c to the 7th power:
c^7
Divide the result by 4, means we divide c^7 by 4
c^7 / 4
Triple what you have means multiply c^7 / 4 by 3
[B]3(c^7 / 4)[/B]

raise f to the 3rd power, then find the quotient of the result and g

raise f to the 3rd power, then find the quotient of the result and g
Take this algebraic expression in two parts:
[LIST=1]
[*]Raise f to the 3rd power means we take f, and write it with an exponent of 3: f^3
[*]Find the quotient of the result and g. We take f^3, and divide it by g
[/LIST]
[B]f^3/g[/B]

raise f to the 8th power then multiply the result by g

f to the 8th power:
f^8
Multiply the result by g
(f^8) * g

Raise f to the 8th power, divide the result by 5, then multiply 10

Raise f to the 8th power, divide the result by 5, then multiply 10
f to the 8th power means we raise f to the power of 8 using an exponent:
f^8
Divide f^8 by 5
(f^8)/5
Now multiply this by 10:
10(f^8)/5
We can simplify this algebraic expression by dividing 10/5 to get 2 on top:
2[B](f^8)[/B]

Raise F to the second power then divide G by the result

Raise F to the second power then divide G by the result
F to the second power:
F^2
Divide G by the result:
[B]G/F^2[/B]

Raise p to the 5th power, then triple the result

Raise p to the 5th power, then triple the result
Raise p to the 5th power:
p^5
Triple the result
[B]3p^5[/B]

Raise p to the 9th power, multiply the result by q, then divide what you have by r

Raise p to the 9th power, multiply the result by q, then divide what you have by r.
Take this in steps:
[LIST]
[*]Raise p to the 9th power: p^9
[*]Multiply the result by q: qp^9
[*]Divide what you have (the result) by r: qp^9/r
[/LIST]
[B](qp^9)/r[/B]

raise q to the 5th power add the result to p then divide what you have by r

raise q to the 5th power add the result to p then divide what you have by r
Take this algebraic expression in parts:
[LIST]
[*]Raise q to the 5th power: q^5
[*]Add the result to p: p + q^5
[*]Divide what you have by r. This means we take our result above and divide it by r:
[/LIST]
[B](p + q^5)/r[/B]

Raise q to the 5th power, then find the quotient of the result and r

Raise q to the 5th power, then find the quotient of the result and r
q to the 5th power:
q^5
Quotient of this and r
[B]q^5/r[/B]

raise r to the 8th power then find the product of the result and 3

raise r to the 8th power then find the product of the result and 3
Raise r to the 8th power means we raise r with an exponent of 8:
r^8
The product of the result and 3 means we muliply r^8 by 3
[B]3r^8[/B]

raise t to the 10th power, then find the quotient of the result and s

raise t to the 10th power, then find the quotient of the result and s
Raise t to the 10th power means we use t as our variable and 10 as our exponent:
t^10
The quotient means a fraction, where the numerator is t^10 and the denominator is s:
[B]t^10/s[/B]

raise the difference of 8 and v to the 7th power

raise the difference of 8 and v to the 7th power
Difference of 8 and v
8 - v
To the 7th power
[B](8 - v)^7[/B]

Raise the difference of V and 7 to the 10th

Raise the difference of V and 7 to the 10th
The difference of V and 7:
V - 7
Raise this to the 10th power:
[B](V - 7)^10[/B]

Raise the sum of k and j to the second power

Raise the sum of k and j to the second power
The sum of k and j is written as:
k + j
Raise the sum to the second power:
[B](k + j)^2[/B]

raise v to the 9th power, then dividethe result by u

V to the 9th power means we use an exponent:
v^9
Divide that result by u
[B]v^9/u[/B]

raise x to the 10th power, then divide b by the result

raise x to the 10th power, then divide b by the result
x to the 10th power
x^10
Divide b by the result:
[B]b/x^10[/B]

raise y to the 10th power, then find the quotient of the result and 2

y to the 10th power means we give y an exponent of 10
y^10
The quotient of y^10 and 2 is:
y^10
-----
2

raise z to the 2nd power, multiply 8 by the result then subtract what you have from 4

raise z to the 2nd power, multiply 8 by the result then subtract what you have from 4
Take this algebraic expression in pieces:
[LIST]
[*]Raise z to the 2nd power: z^2
[*]Multiply by 8: 8z^2
[*]Subtract what you have from 4:
[/LIST]
[B]4 - 8z^2[/B]

ratio of the squares of t and u

ratio of the squares of t and u
Ratio is also known as quotient in algebraic expression problems.
The square of t means we raise t to the power of 2:
t^2
The square of u means we raise u to the power of 2:
u^2
ratio of the squares of t and u means we divide t^2 by u^2:
[B]t^2/u^2[/B]

ratio of x cubed and the sum of y and 5

ratio of x cubed and the sum of y and 5
x cubed means we raise x to the power of 3:
x^3
The sum of y and 5:
y + 5
ratio of x cubed and the sum of y and 5
[B]x^3/(y + 5)[/B]

set of all letters in Australia

set of all letters in Australia
We remove duplicate "a's" and treat A and a as the same letters. Our set S is:
S = [B]{a, i, l, r, s, t, u}[/B]
If we want to find the properties of this set, we visit our [URL='https://www.mathcelebrity.com/powerset.php?num=%7Ba%2Ci%2Cl%2Cr%2Cs%2Ct%2Cu%7D&pl=Show+Power+Set']set notation calculator[/URL].

Sixty-six to the x th power

Sixty-six to the x th power
We raise 66 to the x power:
[B]66^x[/B]

Square root of 9136 divided by 43

Square root of 9136 divided by 43
First, [URL='https://www.mathcelebrity.com/powersq.php?num=sqrt%289136%29&pl=Calculate']take the square root of 9136 in our calculator[/URL]:
4 * sqrt(571)
Now divide this by 43:
[B]4 * sqrt(571) / 43[/B]

Square Roots and Exponents

Given a number (n), or a fraction (n/m), and/or an exponent (x), or product of up to 5 radicals, this determines the following:

* The square root of n denoted as √n

* The square root of the fraction n/m denoted as √n/m

* n raised to the x^{th} power denoted as n^{x} (Write without exponents)

* n raised to the x^{th} power raised to the yth power denoted as (n^{x})^{y} (Write without exponents)

* Product of up to 5 square roots: √a√b√c√d√e

* Write a numeric expression such as 8x8x8x8x8 in exponential form

* The square root of n denoted as √n

* The square root of the fraction n/m denoted as √n/m

* n raised to the x

* n raised to the x

* Product of up to 5 square roots: √a√b√c√d√e

* Write a numeric expression such as 8x8x8x8x8 in exponential form

Start with t and cube it.

Start with t and cube it.
Cubing a variable means raising it to the power of 3:
[B]t^3[/B]

sum of the cube of x and half of y

sum of the cube of x and half of y
The cube of x means we raise x to the 3rd power:
x^3
half of y means we divide y by 2:
y/2
sum of the cube of x and half of y means we add y/2 to x^3
[B]x^3 + y/2[/B]

Sum of the First (n) Numbers

Determines the sum of the first (n)

* Whole Numbers

* Natural Numbers

* Even Numbers

* Odd Numbers

* Square Numbers

* Cube Numbers

* Fourth Power Numbers

* Whole Numbers

* Natural Numbers

* Even Numbers

* Odd Numbers

* Square Numbers

* Cube Numbers

* Fourth Power Numbers

sum of the squares of u and v

sum of the squares of u and v
The square of u means we raise u to the power of 2
u^2
The square of v means we raise v to the power of 2
v^2
The sum means we add v^2 to u^2:
[B]u^2 + v^2[/B]

the cube of c decreased by a^2

the cube of c decreased by a^2
The cube of means we raise the variable c to the power of 3:
c^3
The phrase [I]decreased by[/I] means we subtract:
[B]c^3 - a^2[/B]

The cube of g plus the square of m

The cube of g plus the square of m
The cube of g means we raise g to the 3rd power:
g^3
The square of m means we raise m to the 2nd power:
m^2
The word [I]plus[/I] means we add them both
[B]g^3 + m^2[/B]

The cube of the difference of 5 times the square of y and 7 divided by the square of 2 times y

The cube of the difference of 5 times the square of y and 7 divided by the square of 2 times y
Take this in algebraic expression in parts:
[U]Term 1[/U]
[LIST]
[*]The square of y means we raise y to the 2nd power: y^2
[*]5 times the square of y: 5y^2
[/LIST]
[U]Term 2[/U]
[LIST]
[*]2 times y: 2y
[*]The square of 2 times y: (2y)^2 = 4y^2
[*]7 divide by the square of 2 times y: 7/4y^2
[/LIST]
[U]The difference of these terms is written as Term 1 minus Term 2:[/U]
[LIST]
[*]5y^2/4y^2
[/LIST]
[U]The cube of the difference means we raise the difference to the power of 3:[/U]
[B](5y^2/4y^2)^3[/B]

the cube of the difference of 5 times x and 4

the cube of the difference of 5 times x and 4
Take this algebraic expression in pieces:
5 times x:
5x
The difference of 5x and 4 means we subtract 4 from 5x:
5x - 4
We want to cube this difference, which means we raise the difference to the power of 3.
[B](5x - 4)^3[/B]

the cube of the product of 3 and x

the cube of the product of 3 and x
The product of 3 and x:
3x
Cube this product means raise it to the power of 3:
(3x)^3 = [B]27x^3[/B]

the cube of the sum of 2a and 3b

the cube of the sum of 2a and 3b
Sum of 2a and 3b:
(2a + 3b)
The cube of the sum mean we raise the sum to the power of 3:
[B](2a + 3b)^3[/B]

The cube of x is less than 15

The cube of x is less than 15
The cube of x means we raise x to the 3rd power:
x^3
Less than 15 means we setup the following inequality
[B]x^3 < 15[/B]

The difference between the product of 4 and a number and the square of a number

The difference between the product of 4 and a number and the square of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The product of 4 and a number:
4x
The square of a number means we raise x to the power of 2:
x^2
The difference between the product of 4 and a number and the square of a number:
[B]4x - x^2[/B]

The difference between the square of b and the total of b and 9

The difference between the square of b and the total of b and 9
The square of b means we raise b to the power of 2:
b^2
The total of b and 9 means we add 9 to b:
b + 9
The difference means we subtract:
[B]b^2 - (b + 9)[/B]

The difference between the square of b and the total of d and g

The difference between the square of b and the total of d and g
Square of b means we raise b to the 2nd power:
b^2
Total of d and g:
d + g
The difference between the square of b and the total of d and g
[B]b^2 - (d + g)[/B]

the difference of 5 and the cube of the sum of x and y

the difference of 5 and the cube of the sum of x and y
The sum of x and y:
x + y
The cube of the sum of x and y means we raise x + y to the 3rd power:
(x + y)^3
The difference of 5 and the cube of the sum of x and y
[B]5 - (x + y)^3[/B]

The quotient of 49 and n squared

n squared is written as n to the power of 2, n^2
We have a fraction, where 49 is the numerator, and n^2 is the denominator
49
-----
n^2

the quotient of m squared and a squared

the quotient of m squared and a squared
[U]m squared means we raise m to the power of 2:[/U]
m^2
[U]a squared means we raise a to the power of 2:[/U]
a^2
[U]The [I]quotient[/I] means we divide m^2 by a^2:[/U]
[B]m^2/a^2[/B]

the quotient of the cube of a number x and 5

the quotient of the cube of a number x and 5
[LIST]
[*]A number means an arbitrary variable, let's call it x
[*]The cube of a number means raise it to the 3rd power, so we have x^3
[*]Quotient means we have a fraction, so our numerator is x^3, and our denominator is 5
[/LIST]
[B]x^3
----
5[/B]

the quotient of triple m and n squared

the quotient of triple m and n squared
Triple m means we multiply m by 3:
3m
n squared means we raise n to the 2nd power:
n^2
The quotient is formed as follows:
[B]3m/n^2[/B]

The square of a number added to its reciprocal

The square of a number added to its reciprocal
The phrase [I]a number [/I]means an arbitrary variable, let's call it x.
the square of x mean we raise x to the power of 2. It's written as:
x^2
The reciprocal of x is 1/x
We add these together to get our final algebraic expression:
[B]x^2 + 1/x[/B]

The square of a number increased by 7 is 23

The square of a number increased by 7 is 23
The phrase [I]a number [/I]means an arbitrary variable, let's call it x.
x
The square of a number means we raise x to the power of 2:
x^2
[I]Increased by[/I] means we add 7 to x^2
x^2 + 7
The word [I]is[/I] means an equation. So we set x^2 + 7 equal to 23:
[B]x^2 + 7 = 23[/B]

The square of the difference of n and 2, increased by twice n

The square of the difference of n and 2, increased by twice n
The difference of n and 2:
n - 2
The square of the difference of n and 2 means we raise (n - 2) to the 2nd power:
(n - 2)^2
Twice n means we multiply n by 2:
2n
The square of the difference of n and 2, increased by twice n
[B](n - 2)^2 + 2n[/B]

The square of the radius r

The square of the radius r
The square means you raise r to the power of 2:
[B]r^2[/B]

the square of the sum of 2a and 3b

the square of the sum of 2a and 3b
the sum of 2a and 3b
2a + 3b
The square of this sum means we raise 2a + 3b to the 2nd power:
[B](2a + 3b)^2[/B]

The square of the sum of twice a number x and y

The square of the sum of twice a number x and y
Take this in algebraic expression in 3 parts:
[LIST=1]
[*]Twice a number x means we multiply x by 2: 2x
[*]The sum of twice a number x and y means we add y to 2x above: 2x + y
[*]The square of the sum means we raise the sum (2x + y) to the second power below:
[/LIST]
[B](2x + y)^2[/B]

the square of the sum of two numbers

the square of the sum of two numbers
Let the first number be x. Let the second number be y.
The sum is:
x + y
Now we square that sum by raising the sum to a power of 2:
[B](x + y)^2[/B]

the square of the sum of x and y is less than 20

the square of the sum of x and y is less than 20
The sum of x and y means we add y to x:
x + y
the square of the sum of x and y means we raise the term x + y to the 2nd power:
(x + y)^2
The phrase [I]is less than[/I] means an inequality, so we write this as follows:
[B](x + y)^2 < 20[/B]

The sum of 3 times the square of a number and negative 7

The sum of 3 times the square of a number and negative 7
[U]The phrase [I]a number[/I] means an arbitrary variable, let's call it x:[/U]
x
[U]The square of a number means we raise x to the power of 2:[/U]
x^2
[U]3 times the square of a number:[/U]
3x^2
[U]The sum of 3 times the square of a number and negative 7[/U]
[B]3x^2 - 7[/B]

The sum of 3w and 5 cubed

The sum of 3w and 5 cubed
The sum of 3w and 5:
3w + 5
The word [I]cubed[/I] means we raise 3w + 5 to the power 3:
[B](3w + 5)^3[/B]

The sum Of a number squared and 14

The sum Of a number squared and 14.
A number means an arbitrary variable, let's call it x.
Squared means we raise x to the 2nd power: x^2
The sum means we add x^2 to 14 to get our algebraic expression below:
[B]x^2 + 14[/B]

the sum of the cube of a number and 12

the sum of the cube of a number and 12
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The cube of a number means we raise x to the power of 3:
x^3
Finally, we take the sum of x^3 and 12. Meaning, we add 12 to x^3. This is our final algebraic expression.
[B]x^3 + 12[/B]

the sum of the squares of a and b

the sum of the squares of a and b
Square of a means we raise a to the 2nd power:
a^2
Square of b means we raise b to the 2nd power:
b^2
The sum of squares means we add these terms together to get our algebraic expression:
[B]a^2 + b^2[/B]

The sum of the squares of c and d is 25

The sum of the squares of c and d is 25
The square of c means we we raise c to the power of 2:
c^2
The square of d means we we raise d to the power of 2:
d^2
The sum of the squares of c and d means we add d^2 to c^2:
c^2 + d^2
The word [I]is[/I] means equal to, so we set c^2 + d^2 equal to 25:
[B]c^2 + d^2 = 25[/B]

the sum of x and its cube

the sum of x and its cube
The cube of x means we raise x to the power of 3:
x^3
The sum of x and it's cube means we add x^3 to x:
[B]x + x^3[/B]

the sum of x squared plus y squared

the sum of x squared plus y squared
x squared means we raise x to the power of 2:
x^2
y squared means we raise y to the power of 2:
y^2
The sum means we add both terms together:
[B]x^2 + y^2[/B]

the total of 3 times the cube of u and the square of u

the total of 3 times the cube of u and the square of u
[U]The cube of u means we raise u to the power of 3:[/U]
u^3
[U]The square of u means we raise u to the power of 2:[/U]
u^2
The total of both of these is found by adding them together:
[B]u^3 + u^2[/B]

total of a number and the square of a number

total of a number and the square of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The square of a number means we raise x to the power of 2. x^2
The total means we add x squared to x:
[B]x + x^2[/B]

triple 5, raise the result to the 10th power, then divide p by what you have

triple 5, raise the result to the 10th power, then divide p by what you have
Triple 5, means multiply 5 by 3
3 * 5 --> Simplified, this is 15
Raise the result to the 10th power, means we raise 15 to the 10 power:
15^10
Then divide it by p:
[B]15^10/p[/B]

triple h then raise the result to the 8th power

triple h then raise the result to the 8th power
[U]Triple h means we multiply h by 3:[/U]
3h
[U]Raise the result to the 8th power:[/U]
[B](3h)^8[/B]

tripled square of the difference of a and b

The difference of a and b is written as:
a - b
Square the difference means raise the difference to the power of 2
(a - b)^2
Triple this expression means multiply by 3:
[B]3(a - b)^2[/B]

twenty-nine to the w

twenty-nine to the w
We take 29 and raise it to the w power:
[B]29^w[/B]

twice the square of the product of x and y

twice the square of the product of x and y
Take this algebraic expression in pieces:
[LIST]
[*]The product of x and y means we multiply x and y: xy
[*]The square of the product means we raise xy to the power of 2: (xy)^2 = x^2y^2
[*]Twice the square means we multiply the square by 2: [B]2x^2y^2[/B]
[/LIST]

twice the square of the product of x and y

twice the square of the product of x and y
[LIST]
[*]The product of x and y: xy
[*]The square of the product means we raise xy to the power of 2: (xy)^2
[*]Twice the square means we multiply by 2
[/LIST]
[B]2(xy)^2
or
2x^2y^2[/B]

twice the square root of a number increased by 5 is 23

twice the square root of a number increased by 5 is 23
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
The square root of a number means we raise x to the 1/2 power:
sqrt(x)
the square root of a number increased by 5 means we add 5 to sqrt(x):
sqrt(x) + 5
twice the square root of a number increased by 5 means we multiply sqrt(x) + 5 by 2:
2(sqrt(x) + 5)
The phrase [I]is 23[/I] means we set 2(sqrt(x) + 5) equal to 23:
[B]2(sqrt(x) + 5) = 23[/B]

u cubed equals nine

u cubed equals nine
u cubed means we raise u to the 3rd power:
u^3
We set this equal to 9:
[B]u^3 = 9[/B]

What is an Exponent

This lesson walks you through what an exponent is, the product rule for exponents, the quotient rule for exponents, the 0 power rule, the power of a power rule for exponents

What is the sum of a number x and y raised to the power of two in algebraic expression

What is the sum of a number x and y raised to the power of two in an algebraic expression?
The sum of a number x and y:
x + y
Raise this to the power of 2
(x + y)^2

When 54 is subtracted from the square of a number, the result is 3 times the number.

When 54 is subtracted from the square of a number, the result is 3 times the number.
This is an algebraic expression. Let's take it in parts.
The phrase [I]a number[/I] means an arbitrary variable, let's call it "x".
x
Square the number, means raise it to the 2nd power:
x^2
Subtract 54:
x^2 - 54
The phrase [I]the result[/I] means an equation, so we set x^2 - 54 equal to 3
[B]x^2 - 54 = 3[/B]

When finding the power of a power, you _____________________ the exponents

When finding the power of a power, you _____________________ the exponents
[B]Multiply
[/B]
Example:
(a^b)^c = a^bc

Which of the following can increase power?

Which of the following can increase power?
a. Increasing standard deviation
b. Decreasing standard deviation
c. Increasing both means but keeping the difference between the means constant
d. Increasing both means but making the difference between the means smaller
[B]b. Decreasing standard deviation[/B]
[LIST=1]
[*]Power increases if the standard deviation is smaller.
[*]If the difference between the means is bigger, the power is bigger.
[*]Sample size increase also increases power
[/LIST]

Which of the following could reduce the rate of Type I error? a. Making the significant level from

Which of the following could reduce the rate of Type I error?
a. Making the significant level from 0.01 to 0.05
b. Making the significant level from 0.05 to 0.01
c. Increase the Β level
d. Increase the power
[B]a. Making the significant level from 0.01 to 0.05[/B]
[I]This widens the space under the graph and makes the test less strict.[/I]

Which of the followings is the definition of power? a. Power is the probability of rejecting a null

Which of the followings is the definition of power?
a. Power is the probability of rejecting a null hypothesis
b. Power is the probability of accepting a null hypothesis
c. Power is the probability of accepting a false null hypothesis
d. Power is the probability of rejecting a false null hypothesis
[B]d. Power is the probability of rejecting a false null hypothesis[/B]

Write an equation that relates the quantities. G varies jointly with t and q and inversely with the

Write an equation that relates the quantities. G varies jointly with t and q and inversely with the cube of w . The constant of proportionality is 8.25 .
[LIST]
[*]Varies jointly or directly means we multiply
[*]Varies inversely means divide
[*]The cube of w means we raise w to the 3rd power: w^3
[/LIST]
Using k = 8.25 as our constant of proportionality, we have:
[B]g = 8.25qt/w^3[/B]

x cubed plus x squared decreased by 7

x cubed plus x squared decreased by 7
[U]x cubed means we raise x to the power of 3:[/U]
x^3
[U]x squared means we raise x to the power of 2:[/U]
x^2
[U]x cubed plus x squared[/U]
x^3 + x^2
[U]Decreased by 7:[/U]
[B]x^3 + x^2 - 7[/B]

x squared plus a minus b

x squared plus a minus b
x squared means we raise x to the power of 2:
x^2
Plus a:
x^2 + a
Minus b:
[B]x^2 + a - b[/B]

x squared times the difference of x and y

x squared times the difference of x and y
x squared means we raise x to the power of 2:
x^2
The difference of x and y
x - y
x squared times the difference of x and y
[B]x^2(x - y)[/B]

X to the 9th is less than or equal to 38

X to the 9th is less than or equal to 38:
x to the 9th means 9th power:
x^9
We set this less than or equal 38:
[B]x^9 <= 38[/B]

You and your friend are playing a number-guessing game. You ask your friend to think of a positive n

You and your friend are playing a number-guessing game. You ask your friend to think of a positive number, square the number, multiply the result by 2, and then add three. If your friend's final answer is 53, what was the original number chosen?
Let n be our original number.
Square the number means we raise n to the power of 2:
n^2
Multiply the result by 2:
2n^2
And then add three:
2n^2 + 3
If the friend's final answer is 53, this means we set 2n^2 + 3 equal to 53:
2n^2 + 3 = 53
To solve for n, we subtract 3 from each side, to isolate the n term:
2n^2 + 3 - 3 = 53 - 3
Cancel the 3's on the left side, and we get:
2n^2 = 50
Divide each side of the equation by 2:
2n^2/2 = 50/2
Cancel the 2's, we get:
n^2 = 25
Take the square root of 25
n = +-sqrt(25)
n = +-5
We are told the number is positive, so we discard the negative square root and get:
n = [B]5[/B]

You have $16 and a coupon for a $5 discount at a local supermarket. A bottle of olive oil costs $7.

You have $16 and a coupon for a $5 discount at a local supermarket. A bottle of olive oil costs $7. How many bottles of olive oil can you buy?
A $5 discount gives you $16 + $5 = $21 of buying power.
With olive oil at $7 per bottle, we have $21/$7 = [B]3 bottles of olive oil[/B] you can purchase

You put $5500 in a bond fund which has an annual yield of 4.8%. How much interest will be earned in

You put $5500 in a bond fund which has an annual yield of 4.8%. How much interest will be earned in 23 years?
Build the accumulation of principal. We multiply 5,500 times 1.048 raised to the 23rd power.
Future Value = 5,500 (1.048)^23
Future Value =5,500(2.93974392046)
Future Value = 16,168.59
The question asks for interest earned, so we find this below:
Interest Earned = Future Value - Principal
Interest Earned = 16,168.59 - 5,500
Interest Earned = [B]10,668.59[/B]

z is jointly proportional to the square of x and the cube of y

z is jointly proportional to the square of x and the cube of y
The square of x means we raise x to the power of 2:
x^2
The cube of y means we raise y to the power of 3:
y^3
The phrase [I]jointly proportional[/I] means we have a constant k such that:
[B]z = kx^2y^3[/B]

Z varies jointly as the 4th power of x and the 5th power of y

Z varies jointly as the 4th power of x and the 5th power of y
The 4th power of x means we raise x to the power of 4:
x^4
The 5th power of y means we raise y to the power of 5:
y^5
The phrase [I]varies jointly[/I] means we have a constant k such that:
z = [B]kx^4y^5[/B]

___is the probability of a Type II error; and ___ is the probability of correctly rejecting a false

___is the probability of a Type II error; and ___ is the probability of correctly rejecting a false null hypothesis.
a. 1 - ?; ?
b. ?; 1 - ?;
c. ?; ?;
d. ?; ?
[B]b. ?; 1 - ?;[/B]
[LIST]
[*]H0 is true = Correct Decision 1 - ? Confidence Level = Size of a Test ? = Type I Error
[*]Ho is false = Type II Error ? = Correct Decision 1 - ? = Power of a Test
[/LIST]