1. **State the problem:** Evaluate the expression $4^{-5} \cdot 4^{5}$. 2. **Recall the exponent multiplication rule:** When multiplying powers with the same base, add the exponents: $$a^{m} \cdot a^{n} = a^{m+n}$$ 3. **Apply the rule:** $$4^{-5} \cdot 4^{5} = 4^{-5+5}$$ 4. **Simplify the exponent:** $$4^{0}$$ 5. **Recall the zero exponent rule:** Any nonzero number raised to the zero power equals 1: $$a^{0} = 1$$ 6. **Final answer:** $$4^{-5} \cdot 4^{5} = 1$$