The given expression to simplify is:

[ \frac{\sqrt[3]{(x + 3)^2}}{\sqrt[3]{x - 3}} ]

Steps to Simplify:

1. Combine the cube roots: Using the property of radicals: [ \frac{\sqrt[3]{a}}{\sqrt[3]{b}} = \sqrt[3]{\frac{a}{b}} ] The expression becomes: $\sqrt[3]{\frac{(x + 3)^2}{x - 3}}$

2. Simplify further if possible: Since the cube root is already in simplified form, no further reduction can be made unless additional constraints on $x$ are provided.

Final Simplified Expression:

$\sqrt[3]{\frac{(x + 3)^2}{x - 3}}$

Let me know if you'd like a more detailed explanation or further help!

Follow-Up Questions:

1. What are the domain restrictions for this expression (e.g., values of $x$ for which it is undefined)?
2. How does the cube root affect the positivity/negativity of the result?
3. Can the cube root and exponents be expanded further using logarithmic properties?
4. What happens if $x = 0$ in this expression?
5. How does this differ from a square root simplification?

Tip:

When simplifying radical expressions, always check for properties of exponents and ensure the domain of the expression is considered!