Answer
$\displaystyle \frac{8}{x^{3}y}$
Work Step by Step
We simplify:
$\displaystyle \frac{(4x^{-1}y^{1/3})^{3/2}}{(xy)^{3/2}}=\frac{4^{3/2}(x^{-1})^{3/2}(y^{1/3})^{3/2}}{x^{3/2}y^{3/2}}=
\frac{(4^{1/2})^{3}x^{-3/2}y^{1/2}}{
x^{3/2}y^{3/2}}=2^{3}x^{-3/2-3/2}y^{1/2-3/2}=8x^{-6/2}y^{-2/2}=8x^{-3}y^{-1}=\frac{8}{x^{3}y}$
