How to Divide Powers in Algebra

Dividing Powers

Powers can be divided.

To divide powers, subtract the exponents from each other.

2 to the m divided by 2 to the n equals 2 to the m minus n

This is a law of exponents.

How to Divide Powers

Dividing powers in is easy.

Question

Use the law of exponents to divide the powers below.

2 to the 5 times 2 to the 3

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 5.

    5
  • Find the exponent of the second power. In our example, the second power has an exponent of 3.

    3

3

Subtract the exponents from Step 2 (5 and 3) from each other.

5 − 3 = 2

4

Make the answer from Step 3 (2) the exponent of the base of the powers that have been divided.

2 to the 2

Answer:

We have divided the powers from each other.

2 to the 5 divided by 2 cubed equals 2 squared

Understanding Dividing Powers

Let us look at the rule for dividing powers:

bases and exponents
  • We are dividing 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.

Dividing Powers As a Fraction

A division can be written as a fraction.

2 to the m divided by 2 to the n equals 2 to the m over 2 to the n

Slider

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

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See Also

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