Simplify the Radical Expression fourth root of (2m^7)/(625n^4)

$\sqrt[4]{\frac{2 m^{7}}{625 n^{4}}}$

Rewrite $\frac{2 m^{7}}{625 n^{4}}$ as ${(\frac{m}{5 n})}^{4} (2 m^{3})$ .

Factor the perfect power $m^{4}$ out of $2 m^{7}$ .

$\sqrt[4]{\frac{m^{4} \cdot (2 m^{3})}{625 n^{4}}}$

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

$\sqrt[4]{\frac{m^{4} \cdot (2 m^{3})}{{(5 n)}^{4} \cdot 1}}$

Rearrange the fraction $\frac{m^{4} \cdot (2 m^{3})}{{(5 n)}^{4} \cdot 1}$ .

$\sqrt[4]{{(\frac{m}{5 n})}^{4} (2 m^{3})}$

Pull terms out from under the radical.

$| \frac{m}{5 n} | \sqrt[4]{2 m^{3}}$

Remove non-negative terms from the absolute value.

$\frac{| m |}{5 | n |} \sqrt[4]{2 m^{3}}$

Combine $\frac{| m |}{5 | n |}$ and $\sqrt[4]{2 m^{3}}$ .

$\frac{| m | \sqrt[4]{2 m^{3}}}{5 | n |}$