Simplify cube root of (125x^20)/8

$\sqrt[3]{\frac{125 x^{20}}{8}}$

Rewrite $\frac{125 x^{20}}{8}$ as ${(\frac{5 x^{6}}{2})}^{3} x^{2}$ .

Factor the perfect power ${(5 x^{6})}^{3}$ out of $125 x^{20}$ .

$\sqrt[3]{\frac{{(5 x^{6})}^{3} x^{2}}{8}}$

Factor the perfect power $2^{3}$ out of $8$ .

$\sqrt[3]{\frac{{(5 x^{6})}^{3} x^{2}}{2^{3} \cdot 1}}$

Rearrange the fraction $\frac{{(5 x^{6})}^{3} x^{2}}{2^{3} \cdot 1}$ .

$\sqrt[3]{{(\frac{5 x^{6}}{2})}^{3} x^{2}}$

Pull terms out from under the radical.

$\frac{5 x^{6}}{2} \sqrt[3]{x^{2}}$

Combine $\frac{5 x^{6}}{2}$ and $\sqrt[3]{x^{2}}$ .

$\frac{5 x^{6} \sqrt[3]{x^{2}}}{2}$