d) \( \left(\frac{r^{3} s^{-1}}{s^{-2} r^{-2}}\right)^{-\frac{2}{3}} \)

To simplify the expression \( \left(\frac{r^{3} s^{-1}}{s^{-2} r^{-2}}\right)^{-\frac{2}{3}} \), first rearrange the fraction inside the parentheses. When dividing powers with the same base, we subtract the exponents: \[ \frac{r^{3} s^{-1}}{s^{-2} r^{-2}} = r^{3 - (-2)} s^{-1 - (-2)} = r^{5} s^{1}. \] Now the expression becomes \( (r^{5} s)^{-\frac{2}{3}} \). Applying the power of a power rule, distribute the exponent: \[ (r^{5})^{-\frac{2}{3}} (s)^{-\frac{2}{3}} = r^{-\frac{10}{3}} s^{-\frac{2}{3}}. \] Thus, the simplified expression is: \[ \frac{1}{r^{\frac{10}{3}} s^{\frac{2}{3}}}. \]