To solve the expression $(\frac{3}{2} + 1)^3$, follow these steps:

1. Simplify the expression inside the parentheses: $\frac{3}{2} + 1 = \frac{3}{2} + \frac{2}{2} = \frac{5}{2}$

2. Raise the simplified expression to the power of 3: $\left(\frac{5}{2}\right)^3 = \frac{5^3}{2^3} = \frac{125}{8}$

So, the value of $(\frac{3}{2} + 1)^3$ is $\frac{125}{8}$.

Would you like to see the steps in more detail, or do you have any questions?

Here are some related questions you might be interested in:

1. What is the value of $(\frac{5}{2} - 1)^3$?
2. How do you simplify $(\frac{3}{2} + 1)^2$?
3. What is the cube of $\frac{5}{3}$?
4. How do you convert $\frac{125}{8}$ to a decimal?
5. What is $\left(\frac{7}{3} + \frac{2}{3}\right)^3$?

Tip: When working with fractions, always try to simplify the expression inside the parentheses before applying exponents.