kind of a dumb question but is this right?
e^(-x^2/2a^2) * e^(-x^2/2a^2)
= e^(-2x^2/2a^2) ? would feel a little stupid asking my teacher right now lol
correct, but I'd lose the 2's:
e^(-x^2/a^2)
which is
e^(-x^2/a^2)
ahh thank you. sometimes I just forget how to do the easiest things! lol
No problem! It's always better to ask and clarify any doubts you have.
To simplify the product of two exponential expressions, you need to add their exponents. In this case, we have:
e^(-x^2/2a^2) * e^(-x^2/2a^2)
Using the property of exponents, we can add the exponents:
(-x^2/2a^2) + (-x^2/2a^2)
To add fractions, we need a common denominator, which in this case is 2a^2. So, rewriting the exponents with a common denominator, we get:
(-x^2/2a^2) + (-x^2/2a^2) = -2x^2/2a^2
Now, we can simplify the expression:
-2x^2/2a^2 = -x^2/a^2
So, the correct simplified expression is e^(-x^2/a^2).
I hope that explanation helps! Remember, it's always better to ask and understand rather than making assumptions.