Simplify fourth root of f^8g^7

$\sqrt[4]{f^{8} g^{7}}$

Step 1

Rewrite $f^{8} g^{7}$ as ${(f^{2} g)}^{4} g^{3}$ .

Rewrite $f^{8}$ as ${(f^{2})}^{4}$ .

$\sqrt[4]{{(f^{2})}^{4} g^{7}}$

Factor out $g^{4}$ .

$\sqrt[4]{{(f^{2})}^{4} (g^{4} g^{3})}$

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

$\sqrt[4]{{(f^{2} g)}^{4} g^{3}}$

Step 2

Pull terms out from under the radical.

$f^{2} g \sqrt[4]{g^{3}}$