## How to Divide Powers in Algebra

Dividing powers in algebra is easy.## Question

Use the law of exponents to divide the powers below.## Step-by-Step:

## 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.## Answer:

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**.**a**,^{m}**a**and^{n}**a**are powers.^{m - n} - 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.## Beware

## The Bases Must Be The Same

The law of exponents discussed here only works when the bases are the same. The division below cannot be simplified, and must be left as it is:## Top Tip

## 0, 1 and Negative Exponents

When subtracting exponents, don't worry if the resulting exponent is 0, 1 or negative. The relevant laws of exponents are:- a
^{0}= 1 - a
^{1}= a - a
^{ - n}= 1 / a^{n}

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