# How to Divide Powers in Algebra

## Dividing Powers

Powers can be divided.

To divide powers, subtract the exponents from each other. 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. # 1

Check that the bases of the powers are the same. In our example, the bases are both 2. # 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. • Find the exponent of the second power. In our example, the second power has an exponent of 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. We have divided the powers from each other. ## Understanding Dividing Powers

Let us look at the rule for dividing powers: • 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. ## Slider

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

Open the slider in a new tab