Answer
$2x^{3}y\sqrt[4] (2y)$
Work Step by Step
$\sqrt [4](32x^{12}y^{5})=\sqrt[4] (16\times x^{12}\times y^{4}\times 2y)=\sqrt[4] 16\times \sqrt[4] (x^{12})\times \sqrt [4](y^{4})\times \sqrt[4] (2y)=2x^{3}y\sqrt[4] (2y)$
We know that $\sqrt[4] 16=2$, because $2^{4}=16$. We also know that $\sqrt[4] (x^{12})=x^{3}$, because $(x^{3})^{4}=x^{3\times4}=x^{12}$ and that $\sqrt[4] (y^{4})=y$, because $(y)^{4}=y^{4}$.
