Simplify square root of (y^10)/(9x^6)

$\sqrt{\frac{y^{10}}{9 x^{6}}}$

Step 1

Rewrite $y^{10}$ as ${(y^{5})}^{2}$ .

$\sqrt{\frac{{(y^{5})}^{2}}{9 x^{6}}}$

Step 2

Rewrite $9 x^{6}$ as ${(3 x^{3})}^{2}$ .

$\sqrt{\frac{{(y^{5})}^{2}}{{(3 x^{3})}^{2}}}$

Step 3

Rewrite $\frac{{(y^{5})}^{2}}{{(3 x^{3})}^{2}}$ as ${(\frac{y^{5}}{3 x^{3}})}^{2}$ .

$\sqrt{{(\frac{y^{5}}{3 x^{3}})}^{2}}$

Step 4

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

$\frac{y^{5}}{3 x^{3}}$