## How to Find a Power of an Algebraic Fraction

## Question

Use the law of exponents to find the power with the fraction below.## 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**.## 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.## 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**. It has a base of^{n}**2**with an exponent of**n**. - The bottom of the fraction is a power:
**3**. It has a base of^{n}**3**with an exponent of**n**.

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