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The question in the image asks you to express \( (3^2)^{\frac{3}{2}} \) in its simplest radical form.

Let's break it down:

1. Start by simplifying the expression inside the parentheses: 
   \[
   3^2 = 9
   \]
   
2. Now, the expression becomes:
   \[
   9^{\frac{3}{2}}
   \]

3. The exponent \( \frac{3}{2} \) can be interpreted as:
   \[
   9^{\frac{3}{2}} = \left(9^{\frac{1}{2}}\right)^3
   \]
   
4. \( 9^{\frac{1}{2}} \) is the square root of 9, which is 3:
   \[
   9^{\frac{1}{2}} = \sqrt{9} = 3
   \]

5. Now, raise 3 to the power of 3:
   \[
   3^3 = 27
   \]

So, \( (3^2)^{\frac{3}{2}} \) in its simplest radical form is **27**.

Would you like more details or have any questions?

Here are five related questions to expand your understanding:

1. How would you simplify \( (4^3)^{\frac{2}{3}} \)?
2. What is the radical form of \( 16^{\frac{3}{4}} \)?
3. How do you convert an expression like \( x^{\frac{a}{b}} \) to radical form?
4. What is the value of \( 64^{\frac{2}{3}} \) in simplest radical form?
5. How do you simplify \( (2^4)^{\frac{1}{2}} \)?

**Tip:** When working with fractional exponents, remember that the numerator indicates the power and the denominator indicates the root.

Express \( (3^2)^{\frac{3}{2}} \) in simplest radical form.

Learn how to simplify the expression (3^2)^(3/2) to its simplest radical form with this detailed step-by-step solution. This problem covers exponents and radicals, suitable for students in Grades 9-10.

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