1. The problem involves simplifying and solving expressions with exponents and fractions. 2. Recall the exponent rules: $x^1 = x$, $x^0 = 1$, and any number to the zero power equals 1. 3. Given the expression $x + \frac{3}{5}x + 4$, combine like terms: $x + \frac{3}{5}x = \frac{5}{5}x + \frac{3}{5}x = \frac{8}{5}x$. 4. So the expression simplifies to $\frac{8}{5}x + 4$. 5. The equation $x^1 - 1 = 0$ means $x - 1 = 0$, so $x = 1$. 6. Substitute $x = 1$ into the simplified expression: $\frac{8}{5} \times 1 + 4 = \frac{8}{5} + 4 = \frac{8}{5} + \frac{20}{5} = \frac{28}{5}$. 7. The other expressions $1 + \frac{3}{5} + 4 = \frac{5}{5} + \frac{3}{5} + \frac{20}{5} = \frac{28}{5}$, which matches the previous result. 8. The fractions $\frac{4}{9}$ and $\frac{2}{3}$ are separate values; $\frac{2}{3} = \frac{6}{9}$, which is greater than $\frac{4}{9}$. Final answer: The simplified expression evaluated at $x=1$ is $\frac{28}{5}$.