Simplify cube root of (64x^9)/343

$\sqrt[3]{\frac{64 x^{9}}{343}}$

Rewrite $64 x^{9}$ as ${(4 x^{3})}^{3}$ .

$\sqrt[3]{\frac{{(4 x^{3})}^{3}}{343}}$

Rewrite $343$ as $7^{3}$ .

$\sqrt[3]{\frac{{(4 x^{3})}^{3}}{7^{3}}}$

Rewrite $\frac{{(4 x^{3})}^{3}}{7^{3}}$ as ${(\frac{4 x^{3}}{7})}^{3}$ .

$\sqrt[3]{{(\frac{4 x^{3}}{7})}^{3}}$

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

$\frac{4 x^{3}}{7}$