Answer
$x^{3}y^{3}z^{3}$
Work Step by Step
group like terms
$(\displaystyle \frac{xy^{-2}}{x^{2}y^{-1}z})^{-3}=(\frac{x}{x^{2}}\cdot\frac{y^{-2}}{y^{-1}}\cdot\frac{1}{z})^{-3}=$
... use: $(\displaystyle \frac{a^{m}}{a^{n}}=a^{m-n}),\qquad (\frac{1}{z}=z^{-1})$ ...
$= (x^{1-2}y^{-2-(-1)}z^{-1})^{-3} = (x^{-1}\cdot y^{-1}\cdot z^{-1})^{-3}$
... use $(ab)^{n}=a^{n}b^{n}$
$= x^{-1(-3)}\cdot y^{-1(-3)}\cdot z^{-1(-3)}$
$=x^{3}y^{3}z^{3}$
