Exponential family
What is important to note, and what characterizes all exponential family variants, is that the parameter(s) and the observation variable(s) must factorize (can be separated into products each of which involves only one type of variable), either directly or within either part (the base or exponent) of an exponentiation operation. Generally, this means that all of the factors constituting the density or mass function must be of one of the following forms:
Exponentiation
The term "power" was used by the Greek mathematician Euclid for the square of a line. Archimedes discovered and proved the law of exponents, , necessary to manipulate powers of . In the 9th century, the Persian mathematician Muhammad ibn Mūsā al-Khwārizmī used the terms "mal" for a square and "kahb" for a cube, which later Islamic mathematicians represented in mathematical notation as "m" and "k", respectively, by the 15th century, as seen in the work of Abū al-Hasan ibn Alī al-Qalasādī.