Negative Exponential Function

An exponent is that mathematical term which tells you about the number of time the quantity will be multiplied. If we have a positive power in our Exponential Function then the function will look like e^v. In case of a negative exponential function our function will look like e^-v which can also be written as 1 / e^v. Thus the number of multiplication of a number will be done in the denominator. In case of positive powers, the overall value of the quantity or function increases. Whereas, for negative powered exponent the value of denominator increases but the overall value of the function decreases. Mathematical operations like addition, subtraction, multiplication and division are also possible with these Functions. This can be shown as following,
e^-n + e^-n = 2 e^-n
4e^-n - e^-n = 3 e^-n
e^{- 40n} *e^{- 100n} = e^{-n (40 + 100)} = e^{- 140n}
e^{- 400n} / e^{- 100n} = e^{-n (400 -100)} = e^{- 300n}
 
Let’s consider an example of a function that has negative exponents in it:
F (x) = 4 * x *e²⁰ + 20 (e^-5 * e¹⁰) – (x⁴ * (x^-2 / e⁴),
Solving the above function for some values of x = 10, we get:
F (10) = 4 * 10 * e²⁰ / (20 (e^-5 * e¹⁰) * (10⁴ * (10^-2 / e⁴)),
We need to follow certain rules to solve functions like we should keep in mind the use of brackets (which are solved at first) and also the algebraic operations. So, the function can be solved as:
F (10) = 40 * e²⁰ / (20 (e⁵) * (10² / e⁴)) =40 * e²⁰ / (2000 (e) = 2 * e¹⁹ * 10^-2.