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The expression you provided is:

\[
\frac{e^x}{e^{-x}}
\]

To simplify this expression, we use the property of exponents that states:

\[
\frac{a^m}{a^n} = a^{m-n}
\]

### Simplification:

\[
\frac{e^x}{e^{-x}} = e^{x - (-x)} = e^{x + x} = e^{2x}
\]

### Final Answer:

The simplified expression is:

\[
\boxed{e^{2x}}
\]

Would you like more details on any of these steps, or do you have any further questions? Here are some related questions to deepen your understanding:

1. How do you simplify expressions with exponents when dividing?
2. What happens to an exponent when you subtract a negative exponent?
3. Can you explain why \( e^{2x} \) grows faster than \( e^x \) as \( x \) increases?
4. How would this expression change if the exponent in the denominator were positive?
5. What are some real-world applications of exponential growth, as shown in \( e^{2x} \)?

**Tip:** Always remember that subtracting a negative exponent is equivalent to adding the positive version of that exponent.

Learn how to simplify the expression e^x / e^-x step-by-step. This problem involves exponent rules and exponential functions. Suitable for students in Grades 9-12.

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