1. **Simplify the expression** $\frac{r^6 n^{-7}}{r^4 n^2}$. 2. Use the rule for dividing powers with the same base: $\frac{a^m}{a^n} = a^{m-n}$. 3. Apply this to $r$ and $n$ separately: $$\frac{r^6}{r^4} = r^{6-4} = r^2$$ $$\frac{n^{-7}}{n^2} = n^{-7-2} = n^{-9}$$ 4. Combine the results: $$r^2 n^{-9}$$ 5. Express negative exponents as positive by moving to denominator: $$r^2 \frac{1}{n^9} = \frac{r^2}{n^9}$$ **Final answer:** $$\frac{r^2}{n^9}$$