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How to Find a Power of a Fraction (Mathematics Lesson)

Finding a Power of a Fraction

A power can have an fraction raised to an exponent.

Imagine we have a fraction 23 with an exponent n. We raise both top and bottom of the fraction to the exponent n. This is equal to 2n3n.

This is a laws of exponents.

How to Find a Power of an Algebraic Fraction

An Example Question

Use the law of exponents to find the power with the fraction below.

three quarters squared
Step 1

Find the exponent of the power. In our example, the exponent is 2.

Step 2

Find the top number (called the numerator) of the fraction. In our example, the numerator is 3.

The numerator is 3
Step 3

Raise the number found in Step 2 (3) to the exponent found in Step 1 (2). This becomes the numerator of the answer.

The numerator of the answer is 3 squared
Step 4

Find the bottom number (called the denominator) of the fraction. In our example, the denominator is 4.

The denominator is 4
Step 5

Raise the number found in Step 4 (4) to the exponent found in Step 1 (2). This becomes the denominator of the answer.

The denominator of the answer is 4 squared

We have used the law of exponents to find the power of a fraction.

3 squared over 4 squared

For the final steps, evaluate the powers in our fraction.

Step 6

Evaluate the power on the top of the fraction. In our example, evaluate 32.

32 = 3 × 3 = 9
Step 7

Evaluate the power on the bottom of the fraction. In our example, evaluate 42.

42 = 4 × 4 = 16

(34)2 is equal to 916.

9 over 16

Understanding Finding a Power of a Fraction

Let us look at the rule for powers of a fraction:

bases and exponents

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: 2n. It has a base of 2 with an exponent of n.

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

Another Real Example of How to Find the Power of a Fraction

The slider below shows another real example of how to find the power of a fraction.

Interactive Test
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Here's a second test on finding powers of a fraction.
Here's a third test on finding powers of a fraction.