1. **State the problem:** Simplify the expression $$\frac{1}{e^3}$$ and write it in the form $$a^p$$. 2. **Recall the rule for negative exponents:** For any nonzero number $$a$$ and integer $$n$$, $$\frac{1}{a^n} = a^{-n}$$. 3. **Apply the rule:** $$\frac{1}{e^3} = e^{-3}$$ 4. **Final answer:** $$e^{-3}$$ This is the simplified form in index notation where $$a = e$$ and $$p = -3$$.