Simplify square root of (y^8)/81

$\sqrt{\frac{y^{8}}{81}}$

Step 1

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

$\sqrt{\frac{{(y^{4})}^{2}}{81}}$

Step 2

Rewrite $81$ as $9^{2}$ .

$\sqrt{\frac{{(y^{4})}^{2}}{9^{2}}}$

Step 3

Rewrite $\frac{{(y^{4})}^{2}}{9^{2}}$ as ${(\frac{y^{4}}{9})}^{2}$ .

$\sqrt{{(\frac{y^{4}}{9})}^{2}}$

Step 4

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

$\frac{y^{4}}{9}$