Answer
$\frac{c^2 d \sqrt[3]{25c}}{4}$.
Work Step by Step
The given expression is
$=\sqrt[3]{\frac{25c^7d^3}{64}}$
Use quotient property of cube roots.
$=\frac{\sqrt[3]{25c^7d^3}}{\sqrt[3]{64}}$
Factor as cube terms.
$=\frac{\sqrt[3]{c^6\cdot d^3\cdot 25c}}{\sqrt[3]{64}}$
Use prodcut property of cube roots.
$=\frac{\sqrt[3]{c^6}\cdot \sqrt[3]{d^3}\cdot \sqrt[3]{25c}}{\sqrt[3]{64}}$
Use $64=4^3$.
$=\frac{\sqrt[3]{c^6}\cdot \sqrt[3]{d^3}\cdot \sqrt[3]{25c}}{\sqrt[3]{4^3}}$
Simplify.
$=\frac{c^2\cdot d\cdot \sqrt[3]{25c}}{4}$
$=\frac{c^2 d \sqrt[3]{25c}}{4}$.
