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

The Lesson

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

ab to the n is equal to a to the n times b to the  n 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.
x y squared

Step-by-Step:

1

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

exponent is 2

2

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

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.

x squared

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.

y squared

Answer:

We have found the power of the product.

x squared y squared

Understanding Powers of a Product in Algebra

bases and exponents
  • 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:

    2 x squared is equal to 2 squared x squared
  • When a factor is a term, we can find the power. Notice that the whole term is raised to the exponent:

    x squared y all squared is equal to x squared all squared y squared
  • When a factor is an expression, we can find the power. Notice that the whole expression is raised to the exponent:

    The power of x plus z times y all squared is equal to x plus z all squared times y squared

Lesson Slides

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

What Is a Factor in Algebra?

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

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See Also

What is algebra? The laws of exponents What is a factor? What is a power? What is a base? What is an exponent?