Answer
$\frac{1}{2x^6y^2z}$.
Work Step by Step
The given expression is
$=\frac{4x^{-2}(yz)^{-1}}{2^3x^4y}$
Use the law of exponents $(ab)^n=a^{n}\cdot b^n$
$=\frac{4x^{-2}y^{-1}\cdot z^{-1}}{2^3x^4y}$
Use $4=2^2 $.
$=\frac{2^2}{2^3}\cdot \frac{x^{-2}}{x^4}\cdot \frac{y^{-1}}{y^1}\cdot z^{-1}$
Use the law of exponents $\frac{a^{m}}{a^n}=a^{m-n}$
$=(2^{2-3})\cdot (x^{-2-4})\cdot (y^{-1-1})\cdot (z^{-1})$
Simplify.
$=(2^{-1})\cdot (x^{-6})\cdot (y^{-2})\cdot (z^{-1})$
Use the law of exponents $a^{-n}=\frac{1}{a^{n}}$
$=\frac{1}{2}\cdot \frac{1}{x^{6}}\cdot \frac{1}{y^2}\cdot\frac{1}{ z}$
Simplify.
$=\frac{1}{2x^6y^2z}$.
