Question 82701
simplify by writing with only positive exponents 
(x^2)^-3(x^-2)
______________
(x^2)^-4

Lets first look at each term

{{{((x^2)^(-3))=x^(-6)=1/x^6}}}
{{{(x^(-2))=x^(-2)=1/x^2}}}

{{{(x^2)^(-4)=x^(-8)=1/x^8}}}

We can now write the expression as:

{{{(1/x^6)(1/x^2)/(1/x^8)}}} which equals

{{{(1/x^8)/(1/x^8)=1}}}



CK
{{{(x^(-6))(x(-2))/x(-8)}}} and this equals

{{{x^(-8)/x^(-8)=1}}}

{{{1=1}}}


When multiplying, you add exponents;  when raising to a power, you multiply exponents.


Hope this helps-----ptaylor