Answer
$8xy^{6}$
Work Step by Step
Raising each term in the expression to the power of $3$, we obtain:
$(2x^{\frac{1}{3}}y^{2})^{3}$
=$(2)^{3}(x^{\frac{1}{3}})^{3}(y^{2})^{3}$
=$8(x^{\frac{1}{3}\times3})y^{6}$
=$8(x^{1})(y)^{6}$
=$8xy^{6}$