1. **State the problem:** Simplify the expression $\left(j^4 k^{-1} m^8\right)^{-1}$ using exponent rules. 2. **Recall the rule for negative exponents:** For any base $a$ and exponent $n$, $\left(a^n\right)^{-1} = a^{-n}$. 3. **Apply the negative exponent to each factor inside the parentheses:** $$\left(j^4 k^{-1} m^8\right)^{-1} = j^{-4} k^{1} m^{-8}$$ 4. **Explain:** When raising a product to a power, raise each factor to that power. The negative outside the parentheses changes the sign of each exponent inside. 5. **Final simplified expression:** $$j^{-4} k^{1} m^{-8}$$ This can also be written as: $$\frac{k}{j^{4} m^{8}}$$ which is often preferred to avoid negative exponents.