SAT Practice Exam

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Powers in Fractions

In the following expression

xp  =	√x
	x8

What is p?

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Answer
For problems like these, the most important thing to remember is that when moving a power from the denominator to the numerator, we reverse the sign of the power

In this case, the power of the denominator is 8. Moving it to the numerator, it becomes -8.
The numerator is a square root, which denotes a power of ½

Adding the 2 powers, we get

x^½ - x⁸

Converting 8 to a fraction by multiplying top and bottom by 2, we get
x^½ - x^16/2

Simplifying our powers, we get:

1 - 16
2

-15
2

We have our answer: x^-15/2