Multiplying Powers in Algebra
(KS3, Year 7)

The Lesson

Powers can be multiplied together. To multiply powers, add the exponents together.

a to the m times a to the n equals a to the m plus n This is a law of exponents.

How to Multiply Powers in Algebra

Multiplying powers in algebra is easy.

Question

Use the law of exponents to multiply the powers below.
x squared times x cubed

Step-by-Step:

1

Check that the bases of the powers are the same. In our example, the bases are both x.

x is the base of both powers

2

Find the exponents of the powers
  • Find the exponent of the first power. In our example, the first power has an exponent of 2.

    2
  • Find the exponent of the second power. In our example, the second power has an exponent of 3.

    3

3

Add the exponents from Step 2 (2 and 3).
2 + 3 = 5

4

Make the answer from Step 3 (5) the exponent of the base of the powers that have been multiplied.

x to the 5

Answer:

We have multiplied the powers together.

x squared times x cubed equals x to the 5

Understanding Multiplying Powers in Algebra

Let us look at the rule for multiplying powers in algebra:

bases and exponents
  • We are multiplying powers. am, an and am + n are powers.
  • The base in each power is a. This law of exponents only applies when the bases are the same.
  • The exponents in each power are m, n and m + n. This law of exponents applies even when the exponents are different.

Lesson Slides

The slider below shows another real example of how to multiply powers in algebra. Open the slider in a new tab

Why Does It Work?

Consider the example below.

a squared times a cubed Each term is given by:

a squared equals a times a. a cubed equals a times a times a Multiplying the two together gives:

a times a times a times a times a equals a to the five This shows why the formula given works.

Beware

The Bases Must Be The Same

The law of exponents discussed here only works when the bases are the same. The multiplication below cannot be simplified, and must be left as it is:

a squared times b squared
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See Also

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