Exponentiation
When it is a positive integer, the exponent indicates how many copies of the base are multiplied together. For example, . The base appears times in the repeated multiplication, because the exponent is . Here, is the "base", is the "exponent", and is the "power" or, more specifically, "3 raised to the 5th power".
Exponential dispersion model
In probability and statistics, the class of exponential dispersion models (EDM) is a set of probability distributions that represents a generalisation of the natural exponential family. 
Exponential dispersion models play an important role in statistical theory, in particular in generalized linear models because they have a special structure which enables deductions to be made about appropriate statistical inference. 
There are two versions to formulate an exponential disperson model.
In the univariate case, a real-valued random variable formula_1 belongs to the additive exponential dispersion model with canonical parameter formula_2 and index parameter formula_3, formula_4, if its probability density function can be written as