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 field
A field is an algebraic structure composed of a set of elements, "F", two binary operations, addition (+) such that "F" forms an abelian group with identity 0 and multiplication (·), such that "F" excluding 0 forms an abelian group under multiplication with identity 1, and such that multiplication is distributive over addition, that is for any elements "a", "b", "c" in "F", one has . If there is also a function "E" that maps "F" into "F", and such that for every "a" and "b" in "F" one has
then "F" is called an exponential field, and the function "E" is called an exponential function on "F". Thus an exponential function on a field is a homomorphism between the additive group of "F" and its multiplicative group.