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.