Simplify the Radical Expression fourth root of (x^12y^8)/16

$\sqrt[4]{\frac{x^{12} y^{8}}{16}}$

Step 1

Rewrite $x^{12} y^{8}$ as ${(x^{3} y^{2})}^{4}$ .

$\sqrt[4]{\frac{{(x^{3} y^{2})}^{4}}{16}}$

Step 2

Rewrite $16$ as $2^{4}$ .

$\sqrt[4]{\frac{{(x^{3} y^{2})}^{4}}{2^{4}}}$

Step 3

Rewrite $\frac{{(x^{3} y^{2})}^{4}}{2^{4}}$ as ${(\frac{x^{3} y^{2}}{2})}^{4}$ .

$\sqrt[4]{{(\frac{x^{3} y^{2}}{2})}^{4}}$

Step 4

Pull terms out from under the radical.

$| \frac{x^{3} y^{2}}{2} |$

Step 5

Remove non-negative terms from the absolute value.

$\frac{y^{2} | x^{3} |}{2}$