Simplify (x^-2)/( square root of x^-2)

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

Step 1

Move $x^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Simplify the denominator.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x^{- 2}}$ as $x^{\frac{- 2}{2}}$ .

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

Divide $- 2$ by $2$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{x^{- 1 + 2}}$

Add $- 1$ and $2$ .

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

Step 3

Simplify.

$\frac{1}{x}$