Answer
$2y^{2}\sqrt[3] (2y)$
Work Step by Step
$\sqrt [3](16y^{7})=\sqrt[3] (8y^{6}\times 2y)=\sqrt[3] (8y^{6})\times\sqrt[3] (2y)=2y^{2}\sqrt[3] (2y)$
We know that $\sqrt[3] (8y^{6})=2y^{2}$, because $(2y^{2})^{3}=(2\times2\times2)\times y^{2+2+2}=8y^{6}$.