Simplify the Radical Expression 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.

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

Remove non-negative terms from the absolute value.

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

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

Factor out $e^{4}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

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

$e$ is approximately $2.71828182$ which is positive so remove the absolute value

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