Simplify (1/(x^-2*x^5))^(1/6)

${(\frac{1}{x^{- 2} \cdot x^{5}})}^{\frac{1}{6}}$

Multiply $x^{- 2}$ by $x^{5}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{1}{x^{- 2 + 5}})}^{\frac{1}{6}}$

Add $- 2$ and $5$ .

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

Apply the product rule to $\frac{1}{x^{3}}$ .

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

One to any power is one.

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

Multiply the exponents in ${(x^{3})}^{\frac{1}{6}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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