the other one came out wrong.

Question

8x^2y^-2 (4xy^2)^-1
________ . ___________
x^-2y x^2y

its a fraction and you have to multiply

I assume you mean
[(8x^2 y^-2)/(x^-2 y)] x [(4xy^2)^-1/(x^2 y)]
which can be rewritten
= 8 x^4 y^-3 x [1/(4x^3y^3)]
= 2 x y^-6