1. **State the problem:** Evaluate $$324^{\frac{1}{4}} \cdot \sqrt[4]{\frac{1}{4}}$$. 2. **Rewrite the expression using fractional exponents:** $$324^{\frac{1}{4}} \cdot \left(\frac{1}{4}\right)^{\frac{1}{4}}$$. 3. **Combine the terms under the same root:** Since both have the same root power, multiply inside the root: $$\left(324 \times \frac{1}{4}\right)^{\frac{1}{4}}$$. 4. **Calculate inside the parentheses:** $$324 \times \frac{1}{4} = 81$$. 5. **Now evaluate the fourth root of 81:** $$81^{\frac{1}{4}}$$. 6. **Express 81 as a power of a perfect square:** $$81 = 3^4$$. 7. **Apply the exponent:** $$\left(3^4\right)^{\frac{1}{4}} = 3^{4 \times \frac{1}{4}} = 3^1 = 3$$. **Final answer:** $$3$$.