Question

Square root of xy^2 * fourth root of 16x^4/x^3y^2.

Answer 1

Square root of xy^2 = (xy^2)^(1/2)
= x^(1/2) y

fourth root of 16x^4/x^3y^2 = (16x^4/(x^3 y^2) )^(1/4)
= 2 x^(1/4) y^(-1/2)

so we have:
x^(1/2) y * 2 x^(1/4) y^(-1/2)
= 2 x^(3/4) y^(1/2)