# How to Divide Powers in Algebra

## Dividing Powers in Algebra

Powers can be divided.

To divide powers, subtract the exponents from each other. This is a law of exponents.

## How to Divide Powers in Algebra

Dividing powers in algebra 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 x. # 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 in Algebra

Let us look at the rule for dividing powers in algebra: • We are dividing 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.

## Dividing Powers in Algebra As an Algebraic Fraction

A division in algebra can be written as an algebraic fraction. ## Slider

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

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