Simplify cube root of (27a^3)/(b^6)

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

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

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

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

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

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

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

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

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