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.

three quarters squared

Step-by-Step:

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.

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.

The numerator of the answer is 3 squared

4

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

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.

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.

6

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

32 = 3 × 3 = 9

7

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

42 = 4 × 4 = 16

Answer:

(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.

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See Also

What is a fraction? What is a power? What is a base? What is an exponent? What is a numerator? What is a denominator? The laws of exponents