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The Division Rule


The rule for dividing powers is the opposite of multiplying: If the two powers have the same base, you subtract their exponents from each other. Here is an example to illustrate:

Example 1

Calculate 23 22

You split up the power, 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 = 21 = 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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