Negative Exponent 57Db39
1. Let's start by stating the problem: Why don't two negatives in the exponent of $e$ turn into a positive?
2. The expression involves the exponential function $e^x$, where $x$ is the exponent.
3. Important rule: When multiplying two negative numbers, the result is positive. However, when you have an exponent with a negative sign, it means the reciprocal, not multiplication of negatives.
4. For example, $e^{-a}$ means $\frac{1}{e^a}$, which is the reciprocal of $e^a$.
5. If you have $e^{-(-a)}$, the two negatives in the exponent cancel out, so $e^{-(-a)} = e^a$.
6. But if you have $e^{-a - b}$, the exponent is $-(a + b)$, which is negative, not positive.
7. So, two negatives in the exponent only turn positive if they are negations of each other (like $-(-a)$), not if they are separate negative terms added or subtracted.
Final answer: Two negatives in the exponent turn positive only if they are nested negations, like $-(-a) = a$. Otherwise, the exponent remains negative as per the rules of exponents and signs.