How to Find a Power of a Fraction
Finding a Power of a Fraction
A power can have an fraction raised to an exponent.
This is a laws of exponents.
How to Find a Power of an Algebraic Fraction
Question
Use the law of exponents to find the power with the fraction below.
StepbyStep:
1
Find the exponent of the power. In our example, the exponent is 2.
2
Find the top number (called the numerator) of the fraction. In our example, the numerator is 3.
3
Raise the number found in Step 2 (3) to the exponent found in Step 1 (2). This becomes the numerator of the answer.
4
Find the bottom number (called the denominator) of the fraction. In our example, the denominator is 4.
5
Raise the number found in Step 4 (4) to the exponent found in Step 1 (2). This becomes the denominator of the answer.
We have used the law of exponents to find the power of a fraction.
For the final steps, evaluate the powers in our fraction.
6
Evaluate the power on the top of the fraction. In our example, evaluate 3^{2}.
3^{2} = 3 × 3 = 9
7
Evaluate the power on the bottom of the fraction. In our example, evaluate 4^{2}.
4^{2} = 4 × 4 = 16
Answer:
(^{3}⁄_{4})^{2} is equal to ^{9}⁄_{16}.
Understanding Finding a Power of a Fraction
Let us look at the rule for powers of a fraction:
Firstly, let us look at what is to the left of the equals sign (=):
Let us look at the right hand side of the equals sign (=):

The right hand side is a fraction.

The top of the fraction is a power: 2^{n}. It has a base of 2 with an exponent of n.

The bottom of the fraction is a power: 3^{n}. It has a base of 3 with an exponent of n.