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Finding a Power of a Product in Algebra

(KS3, Year 7)

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.

Step-by-Step:

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. 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

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: