1. **State the problem:** Evaluate the expression $$\left( \frac{r^3 s^{-1}}{r^2 s^6} \right)^{-1}$$ for $$r=8$$ and $$s=-2$$. 2. **Simplify the expression inside the parentheses:** $$\frac{r^3 s^{-1}}{r^2 s^6} = r^{3-2} s^{-1-6} = r^{1} s^{-7} = r s^{-7}$$ 3. **Apply the negative exponent outside:** $$\left(r s^{-7}\right)^{-1} = r^{-1} s^{7}$$ 4. **Substitute the values $$r=8$$ and $$s=-2$$:** $$8^{-1} \times (-2)^7$$ 5. **Calculate each part:** $$8^{-1} = \frac{1}{8}$$ $$(-2)^7 = -128$$ 6. **Multiply the results:** $$\frac{1}{8} \times (-128) = -16$$ **Final answer:** $$-16$$