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The expression given is \( \sqrt[3]{81} \), which represents the cube root of 81.

### Steps to simplify:
1. **Prime factorization of 81**: 
   \[
   81 = 3^4
   \]
2. **Apply the cube root**:
   \[
   \sqrt[3]{3^4} = 3^{4/3}
   \]
   This simplifies as:
   \[
   3^{4/3} = 3 \cdot \sqrt[3]{3}
   \]

### Final answer:
\[
\sqrt[3]{81} = 3 \sqrt[3]{3}
\]

Would you like more details on the simplification process or have any other questions?

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Here are 5 related questions to deepen your understanding:
1. How do you simplify higher-order roots, like the fourth root of a number?
2. What is the general method for simplifying any cube root expression?
3. Can you explain how fractional exponents relate to radical expressions?
4. What is the cube root of other numbers like 64 or 125?
5. How do we calculate cube roots without a calculator?

**Tip:** Always check if the number inside a radical can be factored into smaller powers, as this often makes simplifying easier!

Write the following in simplified radical form: \( \sqrt[3]{81} \)

Learn how to simplify the cube root of 81 using prime factorization and radical rules. This problem provides insights into simplifying cube roots and applying prime factorization to simplify radicals. Suitable for students in Grades 6-8.

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