exponent | MathCelebrity Forum

# exponent

1. ### If 2^x + 2^x + 2^x + 2^x = 2^16, what is the value of x?

If 2^x + 2^x + 2^x + 2^x = 2^16, what is the value of x? Add up the left side, we get: 4(2^x) = 2^16 But 4 = 2^2, so we have: 2^2(2^x) = 2^16 Using our exponent rule, we have: 2^(x + 2) = 2^16 x + 2 = 16 Subtract 2 from each side, we get: x = 14
2. ### Simplify 3^n + 3^n + 3^n

Since we have all coefficients of 3 raised to the n, we have: 3(3^n) Using our exponent rules, we have: 3^(n + 1)
3. ### 3 = b^y. Then 3b = ?

a. b^(y + 1) b. b^(y + 2) c. b^(y + 3) d. b^2y e. b^3y Multiply each side by b: 3b = b^y * b 3b = b^(y + 1) answer A.
4. ### (2x10^3) x (2x10^6) x (2x10^12) = ?

Multiply the 2's together: 2 x 2 x 2 = 8 Multiply the 10 with exponent terms together: 10^3 x 10^6 * 10^12 = 10^(3 + 6 + 12) = 10^21 Group both results: 8 x 10^21
5. ### Find the last digit of 7^2013

Consider the first 8 calculations of 7 to an exponent: 7^1 = 7 7^2 = 49 7^3 = 343 7^4 = 2,401 7^5 = 16,807 7^6 = 117,649 7^7 = 823,543 7^8 = 5,764,801 Take a look at the last digit of the first 8 calculations: 7, 9, 3, 1, 7, 9, 3, 1 The 7, 9, 3, 1 repeats through infinity. So every factor of...
6. ### Find the last digit of 2 raised to the 2020 no calculator

Check out this pattern: 2^1= 2 2^2= 4 2^3 = 8 2^4= 16 2^5 = 32 2^6 = 64 2^7 = 128 2^8 = 256 The last digit repeats itself in blocks of 4 2, 4, 8, 6 We want to know what is the largest number in 1, 2, 3, 4 that divides 2020 without a remainder. LEt's start with 4 and work backwards. 2020/4 =...
7. ### Simplify 6x^2y^3(2x^2y)^3

Simplify the monomial in parentheses: 2^3x^2*3y^3 8x^6y^3 Now we update the multiplication: 6x^2y^3(8x^6y^3) 6*8 x^(2 + 6)y^(3 + 3) 48x^8y^6
8. ### Simplify 2^4 x 8^7

We know that 2^3 = 8, so we can rewrite this as: 2^4 x (2^3)^7 (2^3)^7 = 2^3 * 7 = 2^21 2^4 x 2^21 2^(4 + 21) 2^25
9. ### Given that m is a positive integer and 4^m - 1 = n, which of the following values CANNOT represent n

A. 3 B. 7 C. 63 D. 255 We know that: 4^1 = 4 4^2 = 16 4^3 = 64 4^4 = 256 4^5 = 1024 4^6 = 4096 Notice they all end in 4 or 6. This continues for to infinity. 4^m will either end in a 4 or a 6 Therefore, 4^m - 1 ends in: 4 - 1 = 3 6 - 1 = 5 Choices A, C, and D end in 3 or 5. Choice B...
10. ### Find the last digit of 4^2081 no calculator

Find the last digit of 4^2081 no calculator 4^1= 4 4^2 = 16 4^3 = 64 4^4 = 256 4^5 = 1024 4^6 = 4096 Notice this pattern alternates between odd exponent powers with the result ending in 4 and even exponent powers with the result ending in 6. Since 2081 is odd, the answer is 4.
11. ### 3^14/27^4 = ?

3^14/27^4 = ? Understand that 27 = 3^3. Rewriting this, we have: 3^14/(3^3)^4 Exponent identity states (a^b)^c = a^bc, so we have: 3^14/3^12 Simplifying, we have: 3^(14 - 12) = 3^2 = 9
12. ### 3 power to what gets me 81

3 power to what gets me 81 Let x be our power: 3^x = 81 3 * 3 * 3 * 3 = 81 So x = 4: 3^4 = 81
13. ### A new company is projecting its profits over a number of weeks. They predict that their profits each

A new company is projecting its profits over a number of weeks. They predict that their profits each week can be modeled by a geometric sequence. Three weeks after they started, the company's projected profit is \$10,985.00 Four weeks after they started, the company's projected profit is...
14. ### Bill and nine of his friends each have a lot of money in the bank. Bill has 10^10 dollars in his acc

Bill and nine of his friends each have a lot of money in the bank. Bill has 10^10 dollars in his acc All nine of Bill's friends pooled together is: 9 * 10^9 Bill's 10^10 can be written as 10 * 10^9 So Bill's is greater
15. ### Some scientists believe that there are 10^87 atoms in the entire universe. The number googolplex is

Some scientists believe that there are 10^87 atoms in the entire universe. The number googolplex is a 1 followed by a googol of zeros. If each atom in the universe is used as a zero, how many universes would you need in order to have enough zeros to write out completely the number googolplex...
16. ### If there are 10^30 grains of sand on Beach A, how many grains of sand are there on a beach the has 1

If there are 10^30 grains of sand on Beach A, how many grains of sand are there on a beach the has 10 times the sand as Beach A? (Express your answer using exponents.) 10^30 * 10 = 10^(30 + 1) = 10^31
17. ### 1^10 = ?

1^10 = ? 1^10 = 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 1^10 = 1
18. ### 9, 3, 1, 1/3, 1/9 What is the next number in this sequence? What is the function machine for this se

9, 3, 1, 1/3, 1/9 What is the next number in this sequence? What is the function machine for this sequence? We see the following pattern in this sequence: 9 = 9/3^0 3 = 9/3^1 1 = 9/3^2 1/3 = 9/3^3 1/9 = 9/3^4 Our function machine formula is: f(n) = 9/3^(n - 1) Next term is the 6th term: f(6)...
19. ### 3, 6, 12, 24, 48 What is the function machine for this sequence?

3, 6, 12, 24, 48 What is the function machine for this sequence? We see the following pattern: 3 * 2^0 = 3 3 * 2^1 = 6 3 * 2^2 = 12 3 * 2^3 = 24 3 * 2^4 = 48 Our function machine for term n is: f(n) = 3 * 2^(n - 1)
20. ### 1, 1/2, 1/4, 1/8, 1/16 The next number in the sequence is 1/32. What is the function machine you wou

1, 1/2, 1/4, 1/8, 1/16 The next number in the sequence is 1/32. What is the function machine you would use to find the nth term of this sequence? Hint: look at the denominators We notice that 1/2^0 = 1/1 = 1 1/2^1 = 1/2 1/2^2 = 1/4 1/2^3 = 1/8 1/2^4 = 1/32 So we write our explicit formula for...