Simplify cube root of (63x^5)/(72y^6)

$\sqrt[3]{\frac{63 x^{5}}{72 y^{6}}}$

Reduce the expression $\frac{63 x^{5}}{72 y^{6}}$ by cancelling the common factors.

Factor $9$ out of $63 x^{5}$ .

$\sqrt[3]{\frac{9 (7 x^{5})}{72 y^{6}}}$

Factor $9$ out of $72 y^{6}$ .

$\sqrt[3]{\frac{9 (7 x^{5})}{9 (8 y^{6})}}$

Cancel the common factor.

$\sqrt[3]{\frac{9 (7 x^{5})}{9 (8 y^{6})}}$

Rewrite the expression.

$\sqrt[3]{\frac{7 x^{5}}{8 y^{6}}}$

Rewrite $\frac{7 x^{5}}{8 y^{6}}$ as ${(\frac{x}{2 y^{2}})}^{3} (7 x^{2})$ .

Factor the perfect power $x^{3}$ out of $7 x^{5}$ .

$\sqrt[3]{\frac{x^{3} \cdot (7 x^{2})}{8 y^{6}}}$

Factor the perfect power ${(2 y^{2})}^{3}$ out of $8 y^{6}$ .

$\sqrt[3]{\frac{x^{3} \cdot (7 x^{2})}{{(2 y^{2})}^{3} \cdot 1}}$

Rearrange the fraction $\frac{x^{3} \cdot (7 x^{2})}{{(2 y^{2})}^{3} \cdot 1}$ .

$\sqrt[3]{{(\frac{x}{2 y^{2}})}^{3} (7 x^{2})}$

Pull terms out from under the radical.

$\frac{x}{2 y^{2}} \sqrt[3]{7 x^{2}}$

Combine $\frac{x}{2 y^{2}}$ and $\sqrt[3]{7 x^{2}}$ .

$\frac{x \sqrt[3]{7 x^{2}}}{2 y^{2}}$