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]
