1. The problem is to simplify the expression $$\frac{2^4 - (2^5)^8 - 2^6}{dx}$$. 2. First, note that the expression is written as a fraction with denominator $dx$, which suggests differentiation notation, but since $x$ does not appear in the numerator, we treat $dx$ as a constant denominator for simplification. 3. Simplify the powers inside the numerator: - $2^4 = 16$ - $(2^5)^8 = 2^{5 \times 8} = 2^{40}$ - $2^6 = 64$ 4. Substitute these values back into the numerator: $$16 - 2^{40} - 64$$ 5. Combine the constants: $$16 - 64 = -48$$ 6. So the numerator becomes: $$-48 - 2^{40}$$ 7. The entire expression is: $$\frac{-48 - 2^{40}}{dx}$$ 8. Since $dx$ is just a symbol here and cannot be simplified further, the simplified expression is: $$\boxed{\frac{-48 - 2^{40}}{dx}}$$