1. **State the problem:** Simplify the expression $$\left(\frac{(-4)^3}{(-2)^4}\right)^2$$. 2. **Recall the rules:** - When raising a power to another power, multiply the exponents: $$(a^m)^n = a^{mn}$$. - Negative bases raised to powers: $(-a)^n$ is positive if $n$ is even, negative if $n$ is odd. - Division of powers with the same base: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Calculate numerator and denominator inside the fraction:** - Numerator: $$(-4)^3 = -64$$ because $-4 \times -4 \times -4 = -64$. - Denominator: $$(-2)^4 = 16$$ because $(-2) \times (-2) \times (-2) \times (-2) = 16$. 4. **Form the fraction:** $$\frac{-64}{16}$$ 5. **Simplify the fraction:** $$\frac{-64}{16} = \frac{\cancel{-64}}{\cancel{16}} = -4$$ 6. **Raise the simplified fraction to the power 2:** $$(-4)^2 = 16$$ 7. **Final answer:** $$\boxed{16}$$ Your intermediate step $$\left(\frac{-64}{16}\right)^2$$ is correct, and the final answer is indeed 16.