The expression $\displaystyle {\left({\frac{{{x}^{{2}}{y}^{{3}}{z}^{{3}}{x}^{{-{5}}}}}{{{x}^{{5}}{y}^{{5}}{z}^{{2}}{y}^{{4}}}}}\right)}^{{-{{3}}}}$ equals $\displaystyle {x}^{{r}}{y}^{{s}}{z}^{{t}}$
where $\displaystyle {r}$, the exponent of $\displaystyle {x}$, is:


and $\displaystyle {s}$, the exponent of $\displaystyle {y}$, is:


and finally $\displaystyle {t}$, the exponent of $\displaystyle {z}$, is: