1. The problem asks to find an expression equivalent to $$\frac{3^4}{3^8}$$. 2. Recall the rule for dividing powers with the same base: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. Applying this rule, we get: $$\frac{3^4}{3^8} = 3^{4-8}$$ 4. Simplify the exponent: $$3^{4-8} = 3^{-4}$$ 5. Therefore, the expression equivalent to $$\frac{3^4}{3^8}$$ is $$3^{-4}$$. Answer: $$3^{-4}$$