https://file.aiquickdraw.com/mathbot/file/1726680739476zyhpcu8b.jpg

The image provided contains the mathematical expression:

\[
\frac{e^x}{e^{-2x}} e^5
\]

Let's simplify it step by step:

1. Apply the property of exponents: \(\frac{e^a}{e^b} = e^{a - b}\)
   \[
   \frac{e^x}{e^{-2x}} = e^{x - (-2x)} = e^{x + 2x} = e^{3x}
   \]

2. Now multiply the result by \(e^5\):
   \[
   e^{3x} \cdot e^5 = e^{3x + 5}
   \]

Thus, the simplified expression is:

\[
e^{3x + 5}
\]

Let me know if you would like further details on the steps! Here are some related questions:

1. What are the basic properties of exponents used in simplifying expressions?
2. How do you simplify more complex exponential functions?
3. How do you solve exponential equations in different contexts?
4. Can exponents with different bases be simplified similarly?
5. How do logarithms relate to exponentials in simplifying expressions?

**Tip:** Always remember to combine exponents with the same base by adding or subtracting them based on whether they're multiplied or divided.

Effectuer le calcul suivant : \( \frac{e^x}{e^{-2x}} e^5 \) et donner la réponse sous la forme la plus simple possible.

Learn how to simplify the exponential expression \( \frac{e^x}{e^{-2x}} e^5 \) step by step. This problem explores exponential functions and the laws of exponents, suitable for students in Grades 10-12.

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