Simplify (x^-8*x^-6)^(1/6)

${(x^{- 8} \cdot x^{- 6})}^{\frac{1}{6}}$

Multiply $x^{- 8}$ by $x^{- 6}$ by adding the exponents.

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

${(x^{- 8 - 6})}^{\frac{1}{6}}$

Subtract $6$ from $- 8$ .

${(x^{- 14})}^{\frac{1}{6}}$

Multiply the exponents in ${(x^{- 14})}^{\frac{1}{6}}$ .

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

$x^{- 14 (\frac{1}{6})}$

Cancel the common factor of $2$ .

Factor $2$ out of $- 14$ .

$x^{2 (- 7) \frac{1}{6}}$

Factor $2$ out of $6$ .

$x^{2 \cdot - 7 \frac{1}{2 \cdot 3}}$

Cancel the common factor.

$x^{2 \cdot - 7 \frac{1}{2 \cdot 3}}$

Rewrite the expression.

$x^{- 7 (\frac{1}{3})}$

Combine $- 7$ and $\frac{1}{3}$ .

$x^{\frac{- 7}{3}}$

Move the negative in front of the fraction.

$x^{- \frac{7}{3}}$

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

$\frac{1}{x^{\frac{7}{3}}}$