Simplify the Radical Expression sixth root of 9y^14e^4s^12

$\sqrt[6]{9 y^{14} e^{4} s^{12}}$

Step 1

Rewrite $9 y^{14} e^{4} s^{12}$ as ${(y^{2} s^{2})}^{6} \cdot (9 y^{2} e^{4})$ .

Factor out $y^{12}$ .

$\sqrt[6]{9 (y^{12} y^{2}) e^{4} s^{12}}$

Rewrite $y^{12}$ as ${(y^{2})}^{6}$ .

$\sqrt[6]{9 ({(y^{2})}^{6} y^{2}) e^{4} s^{12}}$

Rewrite $s^{12}$ as ${(s^{2})}^{6}$ .

$\sqrt[6]{9 ({(y^{2})}^{6} y^{2}) e^{4} {(s^{2})}^{6}}$

Move $e^{4}$ .

$\sqrt[6]{9 ({(y^{2})}^{6} y^{2}) {(s^{2})}^{6} e^{4}}$

Move $y^{2}$ .

$\sqrt[6]{9 ({(y^{2})}^{6}) {(s^{2})}^{6} y^{2} e^{4}}$

Move $9$ .

$\sqrt[6]{({(y^{2})}^{6}) {(s^{2})}^{6} \cdot 9 y^{2} e^{4}}$

Rewrite $({(y^{2})}^{6}) {(s^{2})}^{6}$ as ${(y^{2} s^{2})}^{6}$ .

$\sqrt[6]{{(y^{2} s^{2})}^{6} \cdot 9 y^{2} e^{4}}$

Add parentheses.

$\sqrt[6]{{(y^{2} s^{2})}^{6} \cdot 9 (y^{2} e^{4})}$

Add parentheses.

$\sqrt[6]{{(y^{2} s^{2})}^{6} \cdot (9 y^{2} e^{4})}$

Step 2

Pull terms out from under the radical.

$| y^{2} s^{2} | \sqrt[6]{9 y^{2} e^{4}}$

Step 3

Remove non-negative terms from the absolute value.

$y^{2} s^{2} \sqrt[6]{9 y^{2} e^{4}}$

Step 4

Rewrite $9 y^{2} e^{4}$ as ${(3 y e^{2})}^{2}$ .

$y^{2} s^{2} \sqrt[6]{{(3 y e^{2})}^{2}}$

Step 5

Rewrite $\sqrt[6]{{(3 y e^{2})}^{2}}$ as $\sqrt[3]{\sqrt{{(3 y e^{2})}^{2}}}$ .

$y^{2} s^{2} \sqrt[3]{\sqrt{{(3 y e^{2})}^{2}}}$

Step 6

Pull terms out from under the radical.

$y^{2} s^{2} \sqrt[3]{| 3 y e^{2} |}$

Step 7

Remove non-negative terms from the absolute value.

$y^{2} s^{2} \sqrt[3]{3 e^{2} | y |}$