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The question in the image asks to calculate \( 9^{\frac{3}{2}} \). Let's solve it step by step.

### Solution:
The expression \( 9^{\frac{3}{2}} \) is a fractional exponent, which can be interpreted as:

\[
9^{\frac{3}{2}} = \left( 9^{\frac{1}{2}} \right)^3
\]

- \( 9^{\frac{1}{2}} \) is the square root of 9. Since \( \sqrt{9} = 3 \), we get:

\[
9^{\frac{1}{2}} = 3
\]

- Now, raise 3 to the power of 3:

\[
3^3 = 27
\]

### Final Answer:
\[
9^{\frac{3}{2}} = 27
\]

Would you like more details on this, or have any questions?

### Related Questions:
1. How do you solve general fractional exponents like \( x^{\frac{m}{n}} \)?
2. What is the difference between \( x^n \) and \( x^{\frac{1}{n}} \)?
3. How can you simplify expressions with mixed exponents, like \( 8^{\frac{4}{3}} \)?
4. Can you explain how to simplify powers of roots, like \( \left(\sqrt{x}\right)^n \)?
5. What are the applications of fractional exponents in real-world scenarios?

**Tip:** When dealing with fractional exponents, always break them into root and power steps for easier calculations.

Learn how to calculate 9^(3/2) using the concepts of fractional exponents and roots. This problem provides a clear breakdown of exponentiation rules and is suitable for students in Grades 7-9.

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