1. Stating the problem: Simplify and analyze the function $$y=(5-2x)^{-3} + \frac{1}{8} \left(\frac{2}{x} + 1\right)^4$$. 2. Understand each term: The first term is $(5-2x)^{-3}$ which represents the reciprocal cube of $(5-2x)$. 3. The second term is $\frac{1}{8} \left(\frac{2}{x} + 1\right)^4$. Here, we take $(\frac{2}{x} + 1)$, raise it to the 4th power, and multiply by $\frac{1}{8}$. 4. Since the expression involves powers and fractions, proceed carefully with substitution or evaluation at specific $x$ values if needed. Further simplification depends on context or specific tasks (e.g., finding intercepts or derivatives). Final expression remains: $$y = (5-2x)^{-3} + \frac{1}{8} \left(\frac{2}{x} + 1\right)^4$$ This is the simplified form suitable for analysis or graphing.