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

Updated on April 16, 2013

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:


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


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