Simplify fourth root of (81x^15)/625

$\sqrt[4]{\frac{81 x^{15}}{625}}$

Rewrite $\frac{81 x^{15}}{625}$ as ${(\frac{3 x^{3}}{5})}^{4} x^{3}$ .

Factor the perfect power ${(3 x^{3})}^{4}$ out of $81 x^{15}$ .

$\sqrt[4]{\frac{{(3 x^{3})}^{4} x^{3}}{625}}$

Factor the perfect power $5^{4}$ out of $625$ .

$\sqrt[4]{\frac{{(3 x^{3})}^{4} x^{3}}{5^{4} \cdot 1}}$

Rearrange the fraction $\frac{{(3 x^{3})}^{4} x^{3}}{5^{4} \cdot 1}$ .

$\sqrt[4]{{(\frac{3 x^{3}}{5})}^{4} x^{3}}$

Pull terms out from under the radical.

$\frac{3 x^{3}}{5} \sqrt[4]{x^{3}}$

Combine $\frac{3 x^{3}}{5}$ and $\sqrt[4]{x^{3}}$ .

$\frac{3 x^{3} \sqrt[4]{x^{3}}}{5}$