https://file.aiquickdraw.com/mathbot/file/1734078622238vocx8vpo.jpg

The given problem is to simplify the radical expression: 

\[
\sqrt[3]{\frac{x^3}{y^6}}
\]

### Step-by-step solution:
1. **Break the expression inside the cube root into parts:**
   \[
   \sqrt[3]{\frac{x^3}{y^6}} = \frac{\sqrt[3]{x^3}}{\sqrt[3]{y^6}}.
   \]

2. **Simplify each term inside the cube root:**
   - For \(\sqrt[3]{x^3}\): The cube root of \(x^3\) is \(x\).
   - For \(\sqrt[3]{y^6}\): Use the rule \(\sqrt[3]{y^a} = y^{a/3}\). So:
     \[
     \sqrt[3]{y^6} = y^{6/3} = y^2.
     \]

3. **Combine the results:**
   \[
   \frac{\sqrt[3]{x^3}}{\sqrt[3]{y^6}} = \frac{x}{y^2}.
   \]

### Final Answer:
The simplified expression is:
\[
\boxed{\frac{x}{y^2}}
\]

Let me know if you'd like a deeper explanation! 😊

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### Related Questions:
1. How do cube roots differ from square roots in simplifying expressions?
2. What are the general properties of radicals involving fractional exponents?
3. Can you explain how to simplify \(\sqrt[3]{x^5}\)?
4. How do you rationalize denominators involving cube roots?
5. What happens if the numerator or denominator contains a negative exponent?

### Tip:
When simplifying radical expressions, always look for ways to rewrite powers using fractional exponents—they can make the process more straightforward!

Simplify the radical expression \(\sqrt[3]{\frac{x^3}{y^6}}\). Write your answer in the form \(A \sqrt[3]{B}\), or \(A^3 \sqrt[3]{B}\), where A and B are constants or expressions in x and y.

Learn how to simplify the radical expression \(\sqrt[3]{\frac{x^3}{y^6}}\) step by step. This problem involves cube roots, fractional exponents, and simplifying fractions. Suitable for high school students studying Algebra.

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