To evaluate $a^3 b^2$ when $a = 2$ and $b = \frac{3}{4}$, follow these steps:

1. Substitute the values of $a$ and $b$ into the expression:

$a^3 b^2 = (2)^3 \left( \frac{3}{4} \right)^2$

2. Calculate each part:

$2^3 = 2 \times 2 \times 2 = 8$ $\left( \frac{3}{4} \right)^2 = \frac{3^2}{4^2} = \frac{9}{16}$

3. Now multiply the results:

$a^3 b^2 = 8 \times \frac{9}{16} = \frac{8 \times 9}{16} = \frac{72}{16} = 4.5$

So, the value of $a^3 b^2$ when $a = 2$ and $b = \frac{3}{4}$ is $4.5$.

---

Would you like more details on the steps or have any questions?

Here are some related questions you might find interesting:

1. How do you simplify fractions like $\frac{72}{16}$?
2. What happens when both exponents in an expression are fractions?
3. How do powers of a fraction behave with even and odd exponents?
4. How can you generalize the formula for expressions of the form $a^n b^m$?
5. What other types of exponentiation rules are important to know?

Tip: Remember that when multiplying fractions, you simply multiply the numerators and denominators directly.