The equation \(-e^{-x} = 0\) has no solution.

### Explanation:
The exponential function \(e^{-x}\) is always positive for all real values of \(x\). Specifically, \(e^{-x} > 0\) for any \(x\). When multiplied by \(-1\), the result is always negative (i.e., \(-e^{-x} < 0\)).

Thus, \(-e^{-x} = 0\) cannot be true because a negative number can never equal zero.

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Here are 5 related questions:
1. What are the properties of exponential functions?
2. How does the natural exponential function behave as \(x \to \infty\)?
3. How can exponential equations be solved in general?
4. What are some examples of exponential decay in real-life applications?
5. How do you find the inverse of an exponential function?

**Tip:** Remember, exponential functions never result in zero, making them particularly useful for modeling growth and decay that never fully stop.

Understand why the equation -e^-x = 0 has no solution. Explore the properties of exponential functions and learn why they never equal zero. This problem is suitable for high school students in Grades 10-12 studying exponential functions.

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