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The Multiplication Rule


The rule for multiplication with powers is simple: If the two powers have the same base, you add their exponents together. It can best be illustrated by examples.

Example 1

Calculate 23 × 22

If you use the definition of powers, you see that this can be split up like this:

2 × 2 × 2 23 × 2 × 2 22 = 25

You see from this example that all you need to do is to add the exponents:

23 × 22 = 23+2 = 25

Rule

Multiplication of Powers with the Same Base

an × am = an+m

Example 2

Calculate 23 × 22

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

23 × 22 = 23+(2) = 232 = 21 = 2

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