1. The problem is to rewrite the expression $4^{-4}$ without using an exponent. 2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$ where $a \neq 0$ and $n$ is a positive integer. 3. Applying this rule to $4^{-4}$, we get: $$4^{-4} = \frac{1}{4^4}$$ 4. Now calculate $4^4$: $$4^4 = 4 \times 4 \times 4 \times 4 = 256$$ 5. Therefore, the expression without an exponent is: $$\frac{1}{256}$$ This means $4^{-4}$ is the same as one divided by 256.