Answer
$ \displaystyle \frac{1}{2x^{6}y^{2}z}$
Work Step by Step
Apply rule $\quad (a^{m})^{n}=a^{mn},$ and with $2^{3}=8,\qquad $ to obtain
$=\displaystyle \frac{4}{8}\cdot\frac{x^{-2}y^{-1}z^{-1}}{x^{4}y}\\
=\displaystyle \frac{1}{2}\cdot\frac{x^{-2}y^{-1}z^{-1}}{x^{4}y}$
Apply rule $\displaystyle \quad \frac{a^{m}}{a^{n}}=a^{m-n}$:
$=\displaystyle \frac{1}{2}\cdot x^{-2-4}y^{-1-1}z^{-1}$
$=\displaystyle \frac{1}{2}\cdot x^{-6}y^{-2}z^{-1}\qquad$
Apply rule $\displaystyle \quad a^{-m}=\dfrac{1}{a^m}$ to obtain:
$=\displaystyle \frac{1}{2x^{6}y^{2}z}$
