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How to Multiply Powers (Mathematics Lesson)

Multiplying Powers

Powers can be multiplied together.

To multiply powers, add the exponents together.

2 to the m times 2 to the n equals 2 to the m plus n

This is a law of exponents.

How to Multiply Powers

Multiplying powers is easy.

An Example Question

Use the law of exponents to multiply the powers below.

2 squared times 2 cubed
Step 1

Check that the bases of the powers are the same. In our example, the bases are both 2.

2 is the base of both powers
Step 2

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
Step 3

Add the exponents from Step 2 (2 and 3).

2 + 3 = 5
Step 4

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

2 to the 5

We have multiplied the powers together.

2 squared times 2 cubed equals 2 to the 5

Understanding Multiplying Powers

Let us look at the rule for multiplying powers:

bases and exponents
  • We are multiplying powers. 2m, 2n and 2m + n are powers.

  • The base in each power is 2. 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.

A Real Example of How to Multiply Powers

The slider below shows another real example of how to multiply powers.

Interactive Test
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Here's a second test on the multiplying powers.
Here's a third test on multiplying powers.

Note

Why Does It Work?

Consider the example below.

2 squared times 2 cubed

Each term is given by:

2 squared equals 2 times 2. 2 cubed equals 2 times 2 times 2

Multiplying the two together gives:

2 times 2 times 2 times 2 times 2 equals 2 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:

2 squared times 3 squared