To solve $2.3^{\frac{3}{2}}$ and round to the nearest hundredth, follow these steps:

1. Rewrite the expression: $2.3^{\frac{3}{2}}$ means taking the square root of 2.3 and then raising it to the power of 3, or vice versa.

2. Calculate $\sqrt{2.3}$: $\sqrt{2.3} \approx 1.5166$

3. Raise this result to the power of 3: $(1.5166)^3 \approx 3.484$

4. Round to the nearest hundredth: $3.484 \approx 3.48$

Final Answer:

$\boxed{3.48}$

Would you like more details on any of these steps, or have additional questions?

Related Questions:

1. How do you simplify expressions with fractional exponents?
2. What is the difference between square rooting and cubing a number?
3. How can you calculate roots and powers without a calculator?
4. What is the process to round to the nearest hundredth?
5. How does changing the base affect the result of an exponent?

Tip: When dealing with fractional exponents, remember that $a^{\frac{m}{n}} = \sqrt[n]{a^m} = (\sqrt[n]{a})^m$. This can help simplify calculations!