# Finding a Power of a Product in Algebra(KS3, Year 7)

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We can find a power of a product. To find a power of a product, raise each letter in the product to the exponent. This is a law of exponents.

## How to Find the Power of a Product in Algebra

Finding a power of a product in algebra is easy.

## Question

Use the law of exponents to find the power of the product below.

## 1

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

## 2

Find the first letter in the product. In our example, the first letter is x.

## 3

Raise the letter found in Step 2 (x) to the exponent found in Step 1 (2). This becomes the first part of the answer.

## 4

Find the second letter in the product. In our example, the second letter is y.

## 5

Raise the letter found in Step 4 (y) to the exponent found in Step 1 (2). This becomes the second part of the answer.

## Answer:

We have found the power of the product.

## Understanding Powers of a Product in Algebra

• The power is (ab)n.
• The base is the product ab. It is a product because it has factors (a and b) multiplied together. (See Note: What Is a Factor in Algebra?).
ab = a × b
• The exponent is n.
• anbn is a product of the powers an and bn.
anbn = an × bn

## More Examples of Finding the Power of a Product in Algebra

Products in algebra do not just consist of single letters multiplying each other.
• When a factor is a number, we can find the power:
• When a factor is a term, we can find the power. Notice that the whole term is raised to the exponent:
• When a factor is an expression, we can find the power. Notice that the whole expression is raised to the exponent:

## Lesson Slides

The slider below shows another real example of how to find a power of a product in algebra.

## What Is a Factor in Algebra?

A factor is one of the numbers, letters and brackets that are multipled together to make a product.

This page was written by Stephen Clarke.

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