The expression \( \frac{9x^3}{2} \) is already simplified in terms of a rational expression. However, if you're looking for its simplest radical form, this only applies to the part involving \( x^3 \). Let me rewrite it in radical notation.

1. The cube of \( x \) can be expressed as:
\[
x^3 = (x^2 \cdot x) = x^2 \sqrt{x}
\]

So, rewriting the original expression:

\[
\frac{9x^3}{2} = \frac{9x^2 \cdot \sqrt{x}}{2}
\]

Thus, the simplest radical form of \( \frac{9x^3}{2} \) is:

\[
\frac{9x^2 \sqrt{x}}{2}
\]

Would you like further details or explanations on any step?

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Here are five related questions for practice:

1. How do you simplify \( \frac{12x^4}{5} \) in radical form?
2. How do you express \( x^6 \) as a radical expression?
3. Simplify \( \frac{4x^5}{3} \) in its simplest radical form.
4. What is the simplest radical form of \( \frac{8x^3}{7} \)?
5. How would you write \( \frac{15x^2}{4} \) in terms of radicals?

**Tip**: Remember, for expressions involving powers of \( x \), use fractional exponents or radicals for clarity when simplifying complex terms.

Discover how to express 9x^3/2 in its simplest radical form with step-by-step guidance. This solution explores key algebraic concepts like exponents and radicals, suitable for students in Grades 9-11.

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