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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?

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**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!

Evaluate 2.3^(3/2). Round to the nearest hundredth.

Learn how to evaluate the expression 2.3 raised to the power of 3/2 and round the result to the nearest hundredth. This solution includes concepts of fractional exponents and root calculations, suitable for students in Grades 9-10.

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