Simplify sixth root of (m^48n^42)/729

$\sqrt[6]{\frac{m^{48} n^{42}}{729}}$

Rewrite $m^{48} n^{42}$ as ${(m^{8} n^{7})}^{6}$ .

$\sqrt[6]{\frac{{(m^{8} n^{7})}^{6}}{729}}$

Rewrite $729$ as $3^{6}$ .

$\sqrt[6]{\frac{{(m^{8} n^{7})}^{6}}{3^{6}}}$

Rewrite $\frac{{(m^{8} n^{7})}^{6}}{3^{6}}$ as ${(\frac{m^{8} n^{7}}{3})}^{6}$ .

$\sqrt[6]{{(\frac{m^{8} n^{7}}{3})}^{6}}$

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

$\frac{m^{8} n^{7}}{3}$