# Multiplying and Dividing Exponents. What are the rules for multiplying and dividing powers?

## Multiplication And Division Power Rules

The quick rules for multiplying and dividing exponent that have the same base numbers are as follows:

am×an = am+n (so you just need to add the exponents)

am ÷an = am-n(so take the second exponent from the first)

So basically, add the exponents for multiplying and work out the difference for dividing.

Example 1

Simplify x⁷ × x

Since you are multiplying add the exponents:

x⁷ × x = x7+4 = x11

Example 2

Simplify y8 × y

Again you are multiplying the exponents so add them together. Also y has an exponent of 1:

y8 × y = y8+1 = y9

Example 3

Simplify x12 ÷ x9

This time you are dividing the terms so work out the difference:

x12 ÷ x9 = x12-9 = x3

Example 4

Simplify a5/a7

This time you are dividing the terms so work out the difference again:

a5/a7= a5-7 = a-2

Example 5

Simplify x6y2 × x4y10.

Here, you need to add the exponents of the x terms and add the exponents of the y terms:

x6 × x = x10

y2 × y10 = y12

So if you put these together you get a final answer of:

x10 y12

Example 6

Simplify x8y7 ÷ x4y3.

Here, you need to take the exponents of the x terms and also take the exponents of the y terms as you are dividing:

x8 ÷ x4 = x8-4 = x4

Y7 ÷ y3 = y4

So if you put these together you get a final answer of:

x4 y4

Example 7

Simplify 7c6d8e4 × 8c3de-9

This is not as hard as it looks.

First multiply 7 by 8 to give 56 (don’t add these together as they are not exponents). This will go at the start of your answer.

Next work out the exponents of c, d and e by adding the exponents as it’s a multiplication:

c6×c3 = c9

d8×d1 = d9

e4×e-9 = e-5

So if you put all of these answers together you get the expression:

56c9d9e-5

So to summarise, multiplying exponents you add the powers and dividing exponents take the powers.