Answer
$2xy^{2}\sqrt[4] (x^{3}y^{2})$
Work Step by Step
$\sqrt[4] (16x^{7}y^{10})=\sqrt[4] (16\times x^{4}\times y^{8}\times x^{3}y^{2})=\sqrt[4] 16\times \sqrt[4] (x^{4})\times \sqrt[4] (y^{8})\times \sqrt[4] (x^{3}y^{2})=2xy^{2}\sqrt[4] (x^{3}y^{2})$
We know that $\sqrt[4] 16=2$, because $2^{4}=16$.
We know that $\sqrt[4] (x^{4})=x$, because $(x)^{4}=x^{4}$.
We know that $\sqrt[4] (y^{8})=y^{2}$, because $(y^{2})^{4}=y^{2\times4}=y^{8}$.
