Simplify fifth root of f^10g^9

$\sqrt[5]{f^{10} g^{9}}$

Step 1

Rewrite $f^{10} g^{9}$ as ${(f^{2} g)}^{5} g^{4}$ .

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

$\sqrt[5]{{(f^{2})}^{5} g^{9}}$

Factor out $g^{5}$ .

$\sqrt[5]{{(f^{2})}^{5} (g^{5} g^{4})}$

Rewrite ${(f^{2})}^{5} g^{5}$ as ${(f^{2} g)}^{5}$ .

$\sqrt[5]{{(f^{2} g)}^{5} g^{4}}$

Step 2

Pull terms out from under the radical.

$f^{2} g \sqrt[5]{g^{4}}$