Answer
$xy^2$
Work Step by Step
Use the rule $\left(ab\right)^n=a^nb^n$, then simplify to obtain:
$(x^{3}y^{6})^{\frac{1}{3}}=\left(x^{3}\right)^{\frac{1}{3}}\left(y^{6}\right)^{\frac{1}{3}}$
Use the rule $\left(a^m\right)^n=a^{mn}$, then simplify to obtain:
$=x^{3\cdot\frac{1}{3}}y^{6\cdot\frac{1}{3}}$
$=xy^2$
Hence, the correct answer is $xy^2$.
