text: for every nonnegative integer .
  If  is a negative integer,  is defined only if  has a multiplicative inverse. In this case, the inverse of  is denoted , and  is defined as
  Exponentiation with integer exponents obeys the following laws, for  and  in the algebraic structure, and  and  integers:
  These definitions are widely used in many areas of mathematics, notably for groups, rings, fields, square matrices (which form a ring). They apply also to functions from a set to itself, which form a monoid under function composition. This includes, as specific instances, geometric transformations, and endomorphisms of any mathematical structure.
  When there are several operations that may be repeated, it is common to indicate the repeated operation by placing its symbol in the superscript, before the exponent. For example, if  is a real function whose valued can be multiplied,  denotes the exponentiation with respect of multiplication, and  may denote exponentiation with respect of function composition. That is,
  and
  Commonly,  is denoted  while  is denoted
  In a group
  A multiplicative group is a set with as associative operation denoted as multiplication, that has an identity element, and such that every element has an inverse.
  So, if  is a group,  is defined for every  and every integer .