Indices law - law 5 - Raising one power to another power

$(a^m)^n=a^(mn)$

To remember try simple numbers you know first i.e.

First part $(a^m)^n$

$(2^2)^2$

$2^2=4$

$(2^2)^2=(4)^2$

$(4)^2=16$

$(2^2)^2=16$

Second part $a^(mn)$

$2^(2\times2)$

$2^4$

$2\times2\times2\times2=16$

$2^(2\times2)=16$

So yes $(a^m)^n=a^(mn)$

Example

Simplify $(x^3)^2$

Try simple numbers you know first

$(2^3)^2$

$=(2\times2\times2)^2$

$=(8)^2$

$=64$

Ask yourself is this the same as $2^6$

$2^6 = 2\times2\times2\times2\times2\times2$

$2^6=64$

So yes $(2^3)^2=2^6$

Therefore $(x^3)^2=x^6$

Answer:

$(x^3)^2=x^6$