Simplify square root of 9x^-4y^6

$\sqrt{9 x^{- 4} y^{6}}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\sqrt{9 \frac{1}{x^{4}} y^{6}}$

Combine exponents.

Combine $9$ and $\frac{1}{x^{4}}$ .

$\sqrt{\frac{9}{x^{4}} y^{6}}$

Combine $\frac{9}{x^{4}}$ and $y^{6}$ .

$\sqrt{\frac{9 y^{6}}{x^{4}}}$

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

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

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

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

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

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

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

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