Simplify 1/(3 square root of x^-6)

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

Step 1

Simplify the denominator.

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

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

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

$\frac{1}{3 \sqrt{\frac{1^{2}}{x^{6}}}}$

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

$\frac{1}{3 \sqrt{\frac{1^{2}}{{(x^{3})}^{2}}}}$

Rewrite $\frac{1^{2}}{{(x^{3})}^{2}}$ as ${(\frac{1}{x^{3}})}^{2}$ .

$\frac{1}{3 \sqrt{{(\frac{1}{x^{3}})}^{2}}}$

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

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

Step 2

Combine $3$ and $\frac{1}{x^{3}}$ .

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

Step 3

Multiply the numerator by the reciprocal of the denominator.

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

Step 4

Multiply $\frac{x^{3}}{3}$ by $1$ .

$\frac{x^{3}}{3}$