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The Division Rule

The rule for dividing powers is opposite to multiplying. Here is an example to illustrate:

Example 1

Calculate 23 22

You split up the power and cancel equal factors and get:

23 22 = 2 × 2 × 2 2 × 2 = 2 × 2 × 2 2 × 2 = 2.

You see that what has happened is that you have subtracted the exponents:

23 22 = 232 = 2.

Rule

Division of Powers with the Same Base

an am = anm

Example 2

Calculate 25 22

Using the rule above and that () = +, you get

25 22 = 25(2) = 25+2 = 27.

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