Simplify cube root of (-8a^6)/(b^3)

$\sqrt[3]{\frac{- 8 a^{6}}{b^{3}}}$

Move the negative in front of the fraction.

$\sqrt[3]{- \frac{(8) a^{6}}{b^{3}}}$

Rewrite $- \frac{8 a^{6}}{b^{3}}$ as ${(- \frac{2 a^{2}}{b})}^{3}$ .

$\sqrt[3]{{(- \frac{2 a^{2}}{b})}^{3}}$

Pull terms out from under the radical, assuming real numbers.

$- \frac{2 a^{2}}{b}$