Answer
$\frac{\sqrt[3]{2y}}{6y}$
Work Step by Step
The given expression is
$=\sqrt[3]{\frac{1}{108y^2}}$
Factor as cube terms.
$=\sqrt[3]{\frac{1}{27\cdot 4y^2}}$
Multiply by $\frac{\sqrt[3]{2y}}{\sqrt[3]{2y}}$.
$=\sqrt[3]{\frac{1}{27\cdot 4y^2}} \cdot \frac{\sqrt[3]{2y}}{\sqrt[3]{2y}}$
Use product property of cube roots.
$=\sqrt[3]{\frac{2y}{27\cdot 4y^2\cdot 2y}}$
Simplify.
$=\sqrt[3]{\frac{2y}{27\cdot 8y^3}}$
Use quotient property of cube roots.
$=\frac{\sqrt[3]{2y}}{\sqrt[3]{27\cdot 8y^3}}$
Simplify.
$=\frac{\sqrt[3]{2y}}{3\cdot 2y}$
$=\frac{\sqrt[3]{2y}}{6y}$
