1. **State the problem:** Evaluate the expression $\left(\frac{1}{16}\right)^{\frac{1}{4}}$. 2. **Recall the rule:** For any positive number $a$ and rational exponent $\frac{m}{n}$, $a^{\frac{m}{n}} = \sqrt[n]{a^m}$. 3. **Rewrite the base:** $16 = 2^4$, so $\frac{1}{16} = 16^{-1} = 2^{-4}$. 4. **Apply the exponent:** $$\left(\frac{1}{16}\right)^{\frac{1}{4}} = (2^{-4})^{\frac{1}{4}} = 2^{-4 \times \frac{1}{4}} = 2^{-1}$$ 5. **Simplify:** $$2^{-1} = \frac{1}{2}$$ 6. **Final answer:** $$\boxed{\frac{1}{2}}$$