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Examples


Here are two examples where you need to use most of the rules you have learned in the previous lessons. Take the time to really understand these examples and you’ll be on your way to being a master of powers!

Example 1

Simplify a23 a b2 b3 a76 b4

You use the rules for roots, which gives you a23 = a2 3 , a = a1 2 , and a76 = a7 6 . You can also see that b4 = 1 b4.

Put together, these become

a2 3 a1 2 b2 b3 a7 6 1 b4

You use the rules for multiplication and get

a2 3+1 2 b2+3 a7 6 1 b4

You write 2 3 + 1 2 as a single fraction:

2 3 + 1 2 = 2 2 3 2 + 1 3 2 3 = 4 6 + 3 6 = 7 6

2 3 + 1 2 = 2 2 3 2 + 1 3 2 3 = 4 6 + 3 6 = 7 6

That gives you
a7 6 b5 a7 6 b4 = a7 6 b5 a7 6 b4 = b54 = b

Note! b1 = b.

Example 2

Simplify 27 23 (253) 2

Using the power rules you arrive at the following: 27 23 (253) 2 = 27+1 3 25 32 = 221 3 +1 3 210 3 = 222 3 10 3 = 212 3 = 24

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