The expression
(c5d5)13\displaystyle {\left({c}^{{5}}{d}^{{5}}\right)}^{{-\frac{{1}}{{3}}}}

equals 1crds\displaystyle \frac{{1}}{{{c}^{{r}}{d}^{{s}}}} where
r, the exponent of c, is:  
s, the exponent of d, is: