rewrite with positive exponents. assume that even roots are of non negative quantities and that all denominators are non zero (4xy^-2)^-2

4xy^-2 = 4x/y^2

(4x/y^2)^-2 = 1/(4x/y^2)^2
= (y^2/4x)^2
= y^4/16x^2

or, multiplying exponents:

(4xy^-2)^-2 = 4^-2 x^-2 y^4
= y^4/(4^2x^2)
= y^4/16x^2