Simplify cube root of (27x^5)/(64y^9)

$\sqrt[3]{\frac{27 x^{5}}{64 y^{9}}}$

Rewrite $\frac{27 x^{5}}{64 y^{9}}$ as ${(\frac{3 x}{4 y^{3}})}^{3} x^{2}$ .

Factor the perfect power ${(3 x)}^{3}$ out of $27 x^{5}$ .

$\sqrt[3]{\frac{{(3 x)}^{3} x^{2}}{64 y^{9}}}$

Factor the perfect power ${(4 y^{3})}^{3}$ out of $64 y^{9}$ .

$\sqrt[3]{\frac{{(3 x)}^{3} x^{2}}{{(4 y^{3})}^{3} \cdot 1}}$

Rearrange the fraction $\frac{{(3 x)}^{3} x^{2}}{{(4 y^{3})}^{3} \cdot 1}$ .

$\sqrt[3]{{(\frac{3 x}{4 y^{3}})}^{3} x^{2}}$

Pull terms out from under the radical.

$\frac{3 x}{4 y^{3}} \sqrt[3]{x^{2}}$

Combine $\frac{3 x}{4 y^{3}}$ and $\sqrt[3]{x^{2}}$ .

$\frac{3 x \sqrt[3]{x^{2}}}{4 y^{3}}$