Algebra Examples

$\sqrt{\frac{1}{x^{2}}} \cdot \sqrt{\frac{x^{2}}{81}}$

Step 1

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

$\sqrt{\frac{1^{2}}{x^{2}}} \cdot \sqrt{\frac{x^{2}}{81}}$

Step 2

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

$\sqrt{{(\frac{1}{x})}^{2}} \cdot \sqrt{\frac{x^{2}}{81}}$

Step 3

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

$\frac{1}{x} \cdot \sqrt{\frac{x^{2}}{81}}$

Step 4

Rewrite $81$ as $9^{2}$ .

$\frac{1}{x} \cdot \sqrt{\frac{x^{2}}{9^{2}}}$

Step 5

Rewrite $\frac{x^{2}}{9^{2}}$ as ${(\frac{x}{9})}^{2}$ .

$\frac{1}{x} \cdot \sqrt{{(\frac{x}{9})}^{2}}$

Step 6

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

$\frac{1}{x} \cdot \frac{x}{9}$

Step 7

Cancel the common factor of $x$ .

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Step 7.1

Cancel the common factor.

$\frac{1}{x} \cdot \frac{x}{9}$

Step 7.2

Rewrite the expression.

$\frac{1}{9}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{9}$

Decimal Form:

$0.\overline{1}$