Simplify ((4x^-6y^7z^8)/(8x^2y^5z^11))^-1

${(\frac{4 x^{- 6} y^{7} z^{8}}{8 x^{2} y^{5} z^{11}})}^{- 1}$

Move $x^{- 6}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{4 y^{7} z^{8}}{8 x^{2} y^{5} z^{11} x^{6}})}^{- 1}$

Multiply $x^{2}$ by $x^{6}$ by adding the exponents.

Move $x^{6}$ .

${(\frac{4 y^{7} z^{8}}{8 (x^{6} x^{2}) y^{5} z^{11}})}^{- 1}$

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

${(\frac{4 y^{7} z^{8}}{8 x^{6 + 2} y^{5} z^{11}})}^{- 1}$

Add $6$ and $2$ .

${(\frac{4 y^{7} z^{8}}{8 x^{8} y^{5} z^{11}})}^{- 1}$

Cancel the common factor of $4$ and $8$ .

Factor $4$ out of $4 y^{7} z^{8}$ .

${(\frac{4 (y^{7} z^{8})}{8 x^{8} y^{5} z^{11}})}^{- 1}$

Cancel the common factors.

Factor $4$ out of $8 x^{8} y^{5} z^{11}$ .

${(\frac{4 (y^{7} z^{8})}{4 (2 x^{8} y^{5} z^{11})})}^{- 1}$

Cancel the common factor.

${(\frac{4 (y^{7} z^{8})}{4 (2 x^{8} y^{5} z^{11})})}^{- 1}$

Rewrite the expression.

${(\frac{y^{7} z^{8}}{2 x^{8} y^{5} z^{11}})}^{- 1}$

Cancel the common factor of $y^{7}$ and $y^{5}$ .

Factor $y^{5}$ out of $y^{7} z^{8}$ .

${(\frac{y^{5} (y^{2} z^{8})}{2 x^{8} y^{5} z^{11}})}^{- 1}$

Cancel the common factors.

Factor $y^{5}$ out of $2 x^{8} y^{5} z^{11}$ .

${(\frac{y^{5} (y^{2} z^{8})}{y^{5} (2 x^{8} z^{11})})}^{- 1}$

Cancel the common factor.

${(\frac{y^{5} (y^{2} z^{8})}{y^{5} (2 x^{8} z^{11})})}^{- 1}$

Rewrite the expression.

${(\frac{y^{2} z^{8}}{2 x^{8} z^{11}})}^{- 1}$

Cancel the common factor of $z^{8}$ and $z^{11}$ .

Factor $z^{8}$ out of $y^{2} z^{8}$ .

${(\frac{z^{8} y^{2}}{2 x^{8} z^{11}})}^{- 1}$

Cancel the common factors.

Factor $z^{8}$ out of $2 x^{8} z^{11}$ .

${(\frac{z^{8} y^{2}}{z^{8} (2 x^{8} z^{3})})}^{- 1}$

Cancel the common factor.

${(\frac{z^{8} y^{2}}{z^{8} (2 x^{8} z^{3})})}^{- 1}$

Rewrite the expression.

${(\frac{y^{2}}{2 x^{8} z^{3}})}^{- 1}$

Change the sign of the exponent by rewriting the base as its reciprocal.

$\frac{2 x^{8} z^{3}}{y^{2}}$