Answer
$64x^{\frac{3}{4}}y^{\frac{3}{2}}$
Work Step by Step
Raising each term in the expression to the power of $3$, we obtain:
$(4x^{\frac{1}{4}}y^{\frac{1}{2}})^{3}$
=$(4)^{3}(x^{\frac{1}{4}})^{3}(y^{\frac{1}{2}})^{3}$
=$64(x^{\frac{1}{4}\times3})y^{\frac{3}{2}}$
=$64(x^{\frac{3}{4}})(y)^{\frac{3}{2}}$
=$64x^{\frac{3}{4}}y^{\frac{3}{2}}$
