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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 a23ab2b3a76b4

You use the rules for roots, which gives you a23=a23, a=a12, and a76=a76. You can also see that b4=1b4.

Put together, these become

a23a12b2b3a761b4

You use the rules for multiplication and get

a23+12b2+3a761b4

You write 23+12 as a single fraction:

23+12=2232+1323=46+36=76

23+12=2232+1323=46+36=76

That gives you

a76b5a76b4= a76b5 a76b4=b54=b

Note! b1=b.

Example 2

Simplify 2723(253)2

Using the power rules you arrive at the following:

2723(253)2=27+132532=2213+132103=2223103=2123=24

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