1. **State the problem:** Solve the equation $$\frac{2^x y}{2^x 5} + \frac{y}{2} \cdot \frac{x^5}{5} = 10$$ for $y$. 2. **Simplify the first term:** Since $2^x$ appears in both numerator and denominator, they cancel out: $$\frac{\cancel{2^x} y}{\cancel{2^x} 5} = \frac{y}{5}$$ 3. **Rewrite the equation:** $$\frac{y}{5} + \frac{y}{2} \cdot \frac{x^5}{5} = 10$$ 4. **Simplify the second term:** $$\frac{y}{2} \cdot \frac{x^5}{5} = \frac{y x^5}{10}$$ 5. **Combine terms:** $$\frac{y}{5} + \frac{y x^5}{10} = 10$$ 6. **Find common denominator (10):** $$\frac{2y}{10} + \frac{y x^5}{10} = 10$$ 7. **Combine fractions:** $$\frac{2y + y x^5}{10} = 10$$ 8. **Multiply both sides by 10:** $$2y + y x^5 = 100$$ 9. **Factor out $y$:** $$y(2 + x^5) = 100$$ 10. **Solve for $y$:** $$y = \frac{100}{2 + x^5}$$ **Final answer:** $$y = \frac{100}{2 + x^5}$$