# Powers of powers

We know how to multiply and divide powers.

We can also do powers of powers.

For example, what is (*a*^{2})^{4} ?

Remember that* c*^{4} = *c* x *c* x *c* x *c*

(*a*^{2})^{4} =* a*^{2} x *a*^{2} x *a*^{2} x *a*^{2}

=* a*^{2 + 2 + 2 + 2}

= *a*^{8}

So (*a*^{2})^{4} = *a*^{2 x 4}

This property is general

Hence,

(*a** ^{m}*)

*=*

^{n}*a*

^{mn}And since (*a** ^{n}*)

^{m}*=*

*a*and

^{nm}*mn*=

*mn*

It follows that

(*a** ^{m}*)

*= (*

^{n }*a*

*)*

^{n}

^{m}