Simplify fourth root of square root of e^12f^6g^18

$\sqrt[4]{\sqrt{e^{12} f^{6} g^{18}}}$

Rewrite $e^{12} f^{6} g^{18}$ as ${(e^{6} f^{3} g^{9})}^{2}$ .

$\sqrt[4]{\sqrt{{(e^{6} f^{3} g^{9})}^{2}}}$

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

$\sqrt[4]{e^{6} f^{3} g^{9}}$

Rewrite $e^{6} f^{3} g^{9}$ as ${(e g^{2})}^{4} (e^{2} f^{3} g)$ .

Factor out $e^{4}$ .

$\sqrt[4]{e^{4} e^{2} f^{3} g^{9}}$

Factor out $g^{8}$ .

$\sqrt[4]{e^{4} e^{2} f^{3} (g^{8} g)}$

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

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

Move $f^{3}$ .

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

Move $e^{2}$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Pull terms out from under the radical.

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