How to Divide Powers

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This entry is a continuation of Rules 1 and 2 about powers. Rules 3 and 4, presented here, tell you how to divide powers. The next entry will present Rules 5 and 6 about powers of parentheses.

When you have learned these rules, you should practice examples combining the rules.

Rule 3

Rule

Dividing Two Powers with the Same Base

am ÷ an = amn am an = amn

am ÷ an = amnam an = amn

Let’s use an example to see why:

a5 = a a a a a

and

a3 = a a a

This means that

a5 ÷ a3 = (a a a a a) ÷ (a a a) = a a a a a a a a = a a a a a a a a = a2

Example 1

Write x5 ÷ x4 as simply as possible

x5 ÷ x4 = x54 = x1 = x

Write a2 ÷ a5 as simply as possible

a2 ÷ a5 = a25 = a7

Rule 4

Rule

Negative Exponents

an = 1 an

Let’s apply Rule 3 in an example to see why Rule 4 is true:

an = a0n = a0 ÷ an = a0 an = 1 an

Example 2

Write x2 as simply as possible

x2 = 1 x2

Write 1 x5 as simply as possible

1 x5 = x5

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