Simplifying the Exponential Expression $ \frac{e^x}{e^{-2x}} e^5 $

Math Problem Statement

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

The image provided contains the mathematical expression:

$\frac{e^x}{e^{-2x}} e^5$

Let's simplify it step by step:

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

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

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Exponential Functions
Simplification of Expressions

$ \frac{e^a}{e^b} = e^{a - b} $
$ e^a \cdot e^b = e^{a + b} $

Laws of Exponents

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