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Simplify: [tex] e^{ax} \cdot e^{-ax} - e^{2ax} [/tex]

A. [tex] e^{-2ax} [/tex]

B. [tex] e - e^{2ax} [/tex]

C. [tex] 1 - e^{2ax} [/tex]

D. [tex] e^{-2a2x} - e^{2ax} [/tex]

Sagot :

GinnyAnswer
Let's simplify the expression [tex]\( e^{ax} \cdot e^{-ax} - e^{2ax} \)[/tex] step by step.

1. Evaluate [tex]\( e^{ax} \cdot e^{-ax} \)[/tex]:
- Recall the property of exponents that states [tex]\( e^{a} \cdot e^{-a} = e^{a-a} = e^0 = 1 \)[/tex].
- Applying this property to our expression, we get:
[tex]\[ e^{ax} \cdot e^{-ax} = e^{ax-ax} = e^0 = 1 \][/tex]

2. Replace [tex]\( e^{ax} \cdot e^{-ax} \)[/tex] with 1 in the original expression:
- Substitute 1 for [tex]\( e^{ax} \cdot e^{-ax} \)[/tex], so the expression becomes:
[tex]\[ 1 - e^{2ax} \][/tex]

So, the simplified expression is:
[tex]\[ 1 - e^{2ax} \][/tex]

Thus, the correct answer is:
[tex]\[ \boxed{1 - e^{2ax}} \][/tex]
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