The expression $\displaystyle {\left({\frac{{{x}^{{-{{3}}}}{y}^{{-{{1}}}}{z}^{{6}}}}{{{\left({x}{y}\right)}^{{3}}{z}^{{-{{2}}}}}}}\right)}^{{1}}$ 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:
[NOTE: Your answers cannot be algebraic expressions.]