Simplify cube root of (27a^9)/(8b^6)

$\sqrt[3]{\frac{27 a^{9}}{8 b^{6}}}$

Rewrite $27 a^{9}$ as ${(3 a^{3})}^{3}$ .

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

Rewrite $8 b^{6}$ as ${(2 b^{2})}^{3}$ .

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

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

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

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

$\frac{3 a^{3}}{2 b^{2}}$