Algebra Examples

$\frac{1}{x^{\frac{- 3}{6}}}$

Step 1

Reduce the expression $\frac{- 3}{6}$ by cancelling the common factors.

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Step 1.1

Factor $3$ out of $- 3$ .

$\frac{1}{x^{\frac{3 (- 1)}{6}}}$

Step 1.2

Factor $3$ out of $6$ .

$\frac{1}{x^{\frac{3 \cdot - 1}{3 \cdot 2}}}$

Step 1.3

Cancel the common factor.

$\frac{1}{x^{\frac{3 \cdot - 1}{3 \cdot 2}}}$

Step 1.4

Rewrite the expression.

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

Step 2

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

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

Step 3

Move the negative in front of the fraction.

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

Step 4

Multiply $- 1$ by $- 1$ .

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

Step 5

Multiply $\frac{1}{2}$ by $1$ .

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

Step 6

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\sqrt{x^{1}}$

Step 7

Anything raised to $1$ is the base itself.

$\sqrt{x}$