Simplify 1/( cube root of x^-6)

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

Step 1

Simplify the denominator.

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

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

Rewrite $1$ as $1^{3}$ .

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

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

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

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

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

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

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

Step 2

Multiply the numerator by the reciprocal of the denominator.

$1 x^{2}$

Step 3

Multiply $x^{2}$ by $1$ .

$x^{2}$