Simplify square root of x^8y^-6

$\sqrt{x^{8} y^{- 6}}$

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

$\sqrt{x^{8} \frac{1}{y^{6}}}$

Combine $x^{8}$ and $\frac{1}{y^{6}}$ .

$\sqrt{\frac{x^{8}}{y^{6}}}$

Apply basic rules of exponents.

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

$\sqrt{\frac{{(x^{4})}^{2}}{y^{6}}}$

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

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

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

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

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

$\frac{x^{4}}{y^{3}}$