(x^-4y^-2*x^2y^-4)^2
=>(x^-4y^-2*x^2y^-4)^2
a^n*a^m=a^(n+m),multiplying as per this equation within the brackets.
=>(x^-4*x^2*y^-2*y^-4)^2
=>(x^(-4+2)*y^(-2+ -4))^2
=>(x^-2*y^(-2-4))^2
=>(x^-2*y^-6)^2
(x^n)^m=x^(n*m),so (x^n*y^p)^m=x^(n*m)*y^(p*m), from this we can simply the equation as:
=>x^(-2*2)*y^(-6*2)
=>x^-4*y^-12