Subjects algebra

Negative Exponent 57Db39

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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.