Answer
$\frac{5x^3\sqrt[3]{2x^2}}{2}$
Work Step by Step
The given expression is
$=\sqrt[3]{\frac{125x^{11}}{4}}$
Use quotient property of cube roots.
$=\frac{\sqrt[3]{125x^{11}}}{\sqrt[3]{4}}$
Multiply by $\frac{\sqrt[3]{2}}{\sqrt[3]{2}}$.
$=\frac{\sqrt[3]{125x^{11}}}{\sqrt[3]{4}} \cdot \frac{\sqrt[3]{2}}{\sqrt[3]{2}}$
Use product property of cube roots.
$=\frac{\sqrt[3]{125x^{11}\cdot 2}}{\sqrt[3]{4\cdot 2}}$
Simplify.
$=\frac{\sqrt[3]{125x^{11}\cdot 2}}{\sqrt[3]{8}}$
Factor as cube terms.
$=\frac{\sqrt[3]{5^3x^{9}x^2\cdot 2}}{\sqrt[3]{2^3}}$
Use product property of cube roots.
$=\frac{\sqrt[3]{5^3}\sqrt[3]{x^{9}}\sqrt[3]{2x^2}}{\sqrt[3]{2^3}}$
Simplify.
$=\frac{5x^3\sqrt[3]{2x^2}}{2}$
