How to Multiply Powers

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.

Question

Use the law of exponents to multiply the powers below.

2 squared times 2 cubed

Step-by-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

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.

2 to the 5

Answer:

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.

Slider

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

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See Also

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