To solve \(9^{5/2}\):

1. Express \(9\) as \(3^2\):
   \[
   9^{5/2} = (3^2)^{5/2}
   \]

2. Apply the power rule \((a^m)^n = a^{m \times n}\):
   \[
   (3^2)^{5/2} = 3^{2 \times \frac{5}{2}} = 3^5
   \]

3. Calculate \(3^5\):
   \[
   3^5 = 243
   \]

Thus, \(9^{5/2} = 243\).

Would you like more details or have any questions?

Here are some related questions to explore:

1. What is the value of \(9^{3/2}\)?
2. How do you simplify \(16^{3/4}\)?
3. What is the square root of 81?
4. How do you calculate \(27^{4/3}\)?
5. What is the value of \(2^{7/2}\)?
6. How do you simplify \(25^{3/2}\)?
7. What is \(81^{1/4}\)?
8. How do you express \(64^{5/6}\) in simplest form?

**Tip:** When simplifying expressions with exponents, look for opportunities to factor or rewrite the base to make calculations easier.

Learn how to solve the expression 9^(5/2) using exponentiation and power rules. This problem covers fundamental exponentiation concepts and provides a detailed step-by-step solution. Suitable for students in Grades 9-12.

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