Answer
$-\frac{\sqrt[3]{21}}{4ab^2}$
Work Step by Step
The given expression is
$=\sqrt[3]{\frac{21}{-64a^3b^6}}$
Use quotient property of cube roots.
$=\frac{\sqrt[3]{21}}{\sqrt[3]{-64a^3b^6}}$
Use product property of cube roots.
$=\frac{\sqrt[3]{21}}{\sqrt[3]{-64}\cdot \sqrt[3]{a^3}\cdot \sqrt[3]{b^6}}$
Use $-64=(-4)^3$ and $b^6=(b^2)^3$.
$=\frac{\sqrt[3]{21}}{\sqrt[3]{(-4)^3}\cdot \sqrt[3]{a^3}\cdot \sqrt[3]{(b^2)^3}}$
Simplify.
$=\frac{\sqrt[3]{21}}{-4ab^2}$
$=-\frac{\sqrt[3]{21}}{4ab^2}$