Answer
$3xy^{5}\sqrt[4] (2x^{3})$
Work Step by Step
$\sqrt [4](162x^{7}y^{20})=\sqrt[4] (81\times x^{4}\times y^{20}\times 2x^{3})=\sqrt[4] 81\times \sqrt[4] (x^{4})\times \sqrt [4](y^{20})\times \sqrt[4] (2x^{3})=3xy^{5}\sqrt[4] (2x^{3})$
We know that $\sqrt[4] 81=3$, because $3^{4}=81$. We also know that $\sqrt[4] (x^{4})=x$, because $(x)^{4}=x^{4}$ and that $\sqrt[4] (y^{20})=y^{5}$, because $(y^{5})^{4}=y^{4\times5}=y^{20}$.
