Simplify fifth root of n^10m^9

$\sqrt[5]{n^{10} m^{9}}$

Step 1

Rewrite $n^{10} m^{9}$ as ${(n^{2} m)}^{5} m^{4}$ .

Rewrite $n^{10}$ as ${(n^{2})}^{5}$ .

$\sqrt[5]{{(n^{2})}^{5} m^{9}}$

Factor out $m^{5}$ .

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

Rewrite ${(n^{2})}^{5} m^{5}$ as ${(n^{2} m)}^{5}$ .

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

Step 2

Pull terms out from under the radical.

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