To express $9x^{3/2}$ in simplest radical form, follow these steps:

1. Recall that $x^{3/2}$ can be written as a combination of square roots and powers: $x^{3/2} = \sqrt{x^3} = \sqrt{x \cdot x^2} = x\sqrt{x}.$

2. Now multiply by 9: $9x^{3/2} = 9 \cdot x\sqrt{x} = 9x\sqrt{x}.$

Thus, the simplest radical form of $9x^{3/2}$ is: $9x\sqrt{x}.$

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Would you like further details or another explanation?
Here are some related questions you might find useful:

1. How do you simplify expressions with fractional exponents?
2. How do you convert between radical form and exponential form?
3. What are the rules for multiplying and dividing square roots?
4. How do you simplify higher roots (e.g., cube roots)?
5. How does the product property of square roots work?

Tip: Fractional exponents express roots: $x^{m/n} = \sqrt[n]{x^m}$.