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We know how to multiply and divide powers.

We can also do powers of powers.

For example, what is (a2)4 ?

Remember that c4 = c x c x c x c

     (a2)4 = a2 x a2 x a2 x a2

             = a2 + 2 + 2 + 2

             = a8

So (a2)4 = a2 x 4

This property is general

     

 

Hence,

     (am)n = amn

And since (an)m = anm and mn = mn

It follows that

     (am)n = (an)m


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Question 1/5

1. ( (x3 y4)3 )4 is

x10 y11

x24 y32

x12 y20

x36 y48

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