Answer
$\displaystyle \frac{y^{1/2}}{x^{1/4}}$
Work Step by Step
We simplify: $\displaystyle \frac{(xy)^{1/4}(x^{2}y^{2})^{1/2}}{(x^{2}y)^{3/4}}=\frac{x^{1/4}y^{1/4}(x^{2})^{1/2}(y^{2})^{1/2}}{(x^{2})^{3/4}(y)^{3/4}}=\frac{x^{1/4}y^{1/4}x^1y^1}{x^{3/2}y^{3/4}}=x^{1/4+1-3/2}y^{1/4+1-3/4}=x^{1/4+4/4-6/4}y^{1/4+4/4-3/4}=x^{-1/4}y^{2/4}=\frac{y^{1/2}}{x^{1/4}}$
