To solve the expression \( 9^{5/2} \), follow these steps:

### Step 1: Understand the exponent
The exponent \( \frac{5}{2} \) can be interpreted as \( 9^{2.5} \) or as \( \sqrt{9^5} \).

### Step 2: Simplify the expression
Since \( 9 = 3^2 \), we can write:
\[ 9^{5/2} = (3^2)^{5/2} \]

### Step 3: Simplify further using properties of exponents
Using the property \( (a^m)^n = a^{m \cdot n} \), we get:
\[ (3^2)^{5/2} = 3^{2 \cdot \frac{5}{2}} = 3^5 \]

### Step 4: Calculate \( 3^5 \)
\[ 3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243 \]

### Final Answer:
\[ \boxed{243} \]

Would you like more details on any part of the solution?

Here are some related questions to explore further:
1. What is \( 9^2.5 \) without simplifying the base?
2. How do you simplify expressions with exponents involving fractions?
3. What is \( 9^{3/2} \)?
4. What is the value of \( 3^4 \)?
5. How do you simplify \( (a^m)^{n/p} \)?
6. What is \( 9^{1/2} \)?
7. What is the result of \( 9^{-5/2} \)?
8. How does the exponent affect the base in expressions like \( a^{m/n} \)?

**Tip:** Breaking down exponents into smaller parts or using properties of exponents can simplify complex expressions.

Learn how to solve the expression 9^(5/2) with a detailed step-by-step solution. Understand the exponentiation process and apply properties of exponents to simplify the expression effectively. Suitable for students in Grades 9-12.

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