Answer
$ \displaystyle \frac{y^{2}}{x^{1/6}z^{5/4}}$
Work Step by Step
$ \displaystyle \frac{x^{3/2}\cdot y^{4/5}\cdot z^{-3/4}}{x^{5/3}\cdot y^{-6/5}\cdot z^{1/2}}=\qquad$ ....... use $\displaystyle \frac{a^{m}}{a^{n}}=a^{m-n}$
$=x^{3/2-(5/3)}\cdot y^{4/5-(-6/5)}\cdot z^{-3/4-(1/2)}$
... simplify exponents:
$...[\displaystyle \frac{3}{2}-\frac{5}{3}=\frac{3\cdot 3-5\cdot 2}{6}=-\frac{1}{6}]$
$...[-\displaystyle \frac{3}{4}-\frac{1}{2}=\frac{-3-1\cdot 2}{4}=-\frac{5}{4}]$
$=x^{-1/6}\cdot y^{2}\cdot z^{-5/4}\qquad$ ....... use $a^{-n}=\displaystyle \frac{1}{a^{n}}=(\frac{1}{a})^{n}$
$= \displaystyle \frac{y^{2}}{x^{1/6}z^{5/4}}$
