Simplify square root of x^-2

$\sqrt{x^{- 2}}$

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

$\sqrt{\frac{1}{x^{2}}}$

Rewrite $1$ as $1^{2}$ .

$\sqrt{\frac{1^{2}}{x^{2}}}$

Rewrite $\frac{1^{2}}{x^{2}}$ as ${(\frac{1}{x})}^{2}$ .

$\sqrt{{(\frac{1}{x})}^{2}}$

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

$\frac{1}{x}$