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.