Algebra Examples

$\sqrt{\frac{c^{- 1}}{c^{3}}}$

Step 1

Reduce the expression $\frac{c^{- 1}}{c^{3}}$ by cancelling the common factors.

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Step 1.1

Multiply by $1$ .

$\sqrt{\frac{c^{- 1} \cdot 1}{c^{3}}}$

Step 1.2

Factor $c^{- 1}$ out of $c^{3}$ .

$\sqrt{\frac{c^{- 1} \cdot 1}{c^{- 1} c^{4}}}$

Step 1.3

Cancel the common factor.

$\sqrt{\frac{c^{- 1} \cdot 1}{c^{- 1} c^{4}}}$

Step 1.4

Rewrite the expression.

$\sqrt{\frac{1}{c^{4}}}$

Step 2

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

$\sqrt{\frac{1^{2}}{c^{4}}}$

Step 3

Rewrite $c^{4}$ as ${(c^{2})}^{2}$ .

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

Step 4

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

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

Step 5

Pull terms out from under the radical.

$| \frac{1}{c^{2}} |$

Step 6

Remove non-negative terms from the absolute value.

$\frac{| 1 |}{c^{2}}$

Step 7

The absolute value is the distance between a number and zero. The distance between $0$ and $1$ is $1$ .

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