Answer
$\displaystyle \frac{8x^{5/4}}{y^{3/4}}$
Work Step by Step
We simplify:
$\displaystyle \frac{(16x^{2}y^{-1/3})^{3/4}}{(xy^2)^{1/4}}=\frac{16^{3/4}(x^{2})^{3/4}(y^{-1/3})^{3/4}}{x^{1/4}(y^{2})^{1/4}}
=\frac{(16^{1/4})^{3}x^{3/2}y^{-1/4}}{x^{1/4}y^{2/4}}=2^{3}x^{3/2-1/4}y^{-1/4-2/4}=8x^{5/4}y^{-3/4}=\frac{8x^{5/4}}{y^{3/4}}$
