1. **State the problem:** Simplify the expression $$r \cdot r^{-8} \cdot r^{-4}$$ and write the result using positive exponents. 2. **Recall the exponent rule:** When multiplying powers with the same base, add the exponents: $$a^m \cdot a^n = a^{m+n}$$ 3. **Apply the rule:** $$r \cdot r^{-8} \cdot r^{-4} = r^{1} \cdot r^{-8} \cdot r^{-4} = r^{1 + (-8) + (-4)}$$ 4. **Simplify the exponent:** $$1 + (-8) + (-4) = 1 - 8 - 4 = -11$$ 5. **Write the expression:** $$r^{-11}$$ 6. **Convert to positive exponent:** $$r^{-11} = \frac{1}{r^{11}}$$ **Final answer:** $$\frac{1}{r^{11}}$$