Question 58651
Some rules we will use:
1. {{{highlight((a^m*b^n)^t=a^(mt)*b^(nt))}}}
2.  {{{highlight(a^(-m)=1/a^m)}}}
3.  {{{highlight(1/a^(-m)=a^m)}}}
4.  {{{highlight(a^m*a^n=a^(m+n))}}}
:
{{{(a^2x^(-2))^(-2)/(a^(-3)x^2)^(-2)}}}  Rule 1
{{{(a^(-4)x^4)/(a^6x^(-4))}}}  Rule 2 and 3.
{{{x^4*x^4/(a^4*a^6)}}}  Rule 4
{{{highlight(x^8/a^10)}}}
:
Happy Calculating!!!