1. The problem asks to rewrite the expression $3^{-4}$ 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 $3^{-4}$, we get: $$3^{-4} = \frac{1}{3^4}$$ 4. Now calculate $3^4$: $$3^4 = 3 \times 3 \times 3 \times 3 = 81$$ 5. Substitute back: $$3^{-4} = \frac{1}{81}$$ 6. Therefore, the expression $3^{-4}$ rewritten without an exponent is $\frac{1}{81}$. Final answer: $\frac{1}{81}$