Answer
$-\frac{3\sqrt[3]{3y^2}}{10x}$.
Work Step by Step
The given expression is
$=-\sqrt[3]{\frac{81y^2}{1000x^3}}$
Use quotient property of cube roots.
$=-\frac{\sqrt[3]{81y^2}}{\sqrt[3]{1000x^3}}$
Factor as cube terms.
$=-\frac{\sqrt[3]{27\cdot 3y^2}}{\sqrt[3]{1000x^3}}$
Use product property of cube roots.
$=-\frac{\sqrt[3]{27}\sqrt[3]{y^2}}{\sqrt[3]{1000}\cdot \sqrt[3]{x^3}}$
Use $27=3^3$ and $1000=10^3$.
$=-\frac{\sqrt[3]{3^3}\sqrt[3]{y^2}}{\sqrt[3]{1000}\cdot \sqrt[3]{x^3}}$
Simplify.
$=-\frac{3\sqrt[3]{3y^2}}{10x}$.
