Answer
$2y^{3}\sqrt[3] (5y)$
Work Step by Step
$\sqrt [3] (40y^{10})=\sqrt [3] (8y^{9}\times5y)=\sqrt [3] (8y^{9})\times \sqrt[3] (5y)=2y^{3}\sqrt[3] (5y)$
We know that $\sqrt[3] (8y^{9})=2y^{3}$, because $(2y^{3})^{3}=(2\times2\times2)\times y^{3\times3}=8y^{9}$.
