1. **State the problem:** Evaluate the expression $$\left(1024^{\frac{1}{4}}\right)^{\frac{4}{5}}$$ and select the correct answer from the choices: -4, 4, 256, -256. 2. **Recall the exponent rule:** When raising a power to another power, multiply the exponents: $$\left(a^{m}\right)^{n} = a^{m \times n}$$ 3. **Apply the rule:** $$\left(1024^{\frac{1}{4}}\right)^{\frac{4}{5}} = 1024^{\frac{1}{4} \times \frac{4}{5}} = 1024^{\frac{4}{20}} = 1024^{\frac{1}{5}}$$ 4. **Simplify the base:** Note that $$1024 = 2^{10}$$, so: $$1024^{\frac{1}{5}} = \left(2^{10}\right)^{\frac{1}{5}} = 2^{10 \times \frac{1}{5}} = 2^{2}$$ 5. **Calculate the final value:** $$2^{2} = 4$$ **Final answer:** 4 Therefore, the correct choice is **B**.