Answer
$3y^3\sqrt[3]{2y}$
Work Step by Step
Recall the property (pg. 367):
$\sqrt[n]{a}\cdot \sqrt[n]{b}=\sqrt[n]{ab}$ (if $\sqrt[n]{a}$ and $\sqrt[n]{b}$ are real numbers)
Applying this property, the given expression simplifies to:
$=\sqrt[3]{27\cdot y^{9}\cdot 2y}$
$=\sqrt[3]{3^3\cdot \left(y^3\right)^3\cdot 2y}$
$=\sqrt[3]{3^3}\cdot \sqrt[3]{\left(y^3\right)^3} \cdot\sqrt[3]{2y}$
$=3\cdot y^3 \cdot \sqrt[3]{2y}$
$=3y^3\sqrt[3]{2y}$