Simplify cube root of f^6g^5

$\sqrt[3]{f^{6} g^{5}}$

Step 1

Rewrite $f^{6} g^{5}$ as ${(f^{2} g)}^{3} g^{2}$ .

Rewrite $f^{6}$ as ${(f^{2})}^{3}$ .

$\sqrt[3]{{(f^{2})}^{3} g^{5}}$

Factor out $g^{3}$ .

$\sqrt[3]{{(f^{2})}^{3} (g^{3} g^{2})}$

Rewrite ${(f^{2})}^{3} g^{3}$ as ${(f^{2} g)}^{3}$ .

$\sqrt[3]{{(f^{2} g)}^{3} g^{2}}$

Step 2

Pull terms out from under the radical.

$f^{2} g \sqrt[3]{g^{2}}$