Algebra Examples

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

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.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

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

Step 3

Combine $\frac{1}{x}$ and $x^{2}$ .

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

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Reduce the expression $\frac{x^{2}}{x}$ by cancelling the common factors.

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Step 4.1.1

Factor $x$ out of $x^{2}$ .

$\frac{1}{\frac{x \cdot x}{x}}$

Step 4.1.2

Raise $x$ to the power of $1$ .

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

Step 4.1.3

Factor $x$ out of $x^{1}$ .

$\frac{1}{\frac{x \cdot x}{x \cdot 1}}$

Step 4.1.4

Cancel the common factor.

$\frac{1}{\frac{x \cdot x}{x \cdot 1}}$

Step 4.1.5

Rewrite the expression.

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

Step 4.2

Divide $x$ by $1$ .

$\frac{1}{x}$