#### Answer

$\sqrt[3]{128y^{10}}=4y^{3}\sqrt[3]{2y}$

#### Work Step by Step

$\sqrt[3]{128y^{10}}$
Take the cubic root of each factor:
$\sqrt[3]{128y^{10}}=\sqrt[3]{128}\cdot\sqrt[3]{y^{10}}=...$
Rewrite $128$ as $64\cdot2$ and simplify:
$...=\sqrt[3]{64\cdot2}\cdot\sqrt[3]{y^{10}}=(4\sqrt[3]{2})(y^{3}\sqrt[3]{y})=4y^{3}\sqrt[3]{2y}$