## The Lesson

A power can have an fraction raised to an exponent. This is a laws of exponents.

## Question

Use the law of exponents to find the power with the fraction below. # 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 32.
32 = 3 × 3 = 9

# 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. ## 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: 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.

## Lesson Slides

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