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The expression given is \(-\sqrt[5]{32}\).

To simplify this, follow these steps:

1. **Identify the fifth root**:
   \[
   \sqrt[5]{32}
   \]
   \(32\) can be expressed as \(2^5\). So:
   \[
   \sqrt[5]{32} = \sqrt[5]{2^5} = 2
   \]

2. **Apply the negative sign**:
   The expression simplifies to:
   \[
   -\sqrt[5]{32} = -2
   \]

So, the simplified form of \(-\sqrt[5]{32}\) is \(-2\).

Would you like further details or have any questions?

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Here are 5 follow-up questions to deepen your understanding:

1. What is the general process for simplifying an expression involving a radical with an index higher than 2?
2. How would you simplify \(\sqrt[5]{-32}\) and why?
3. Can you explain why \(\sqrt[5]{32} = 2\)?
4. What would be the simplified form of \(\sqrt[5]{243}\)?
5. How does the process change if the radical was a square root instead of a fifth root?

**Tip:** When simplifying radicals, express the number under the root as a power to match the root's index, if possible.

Learn how to simplify the expression -√(5)32, focusing on radicals and exponent properties. This step-by-step solution is suitable for high school students, covering key concepts such as nth roots and negative exponents.

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