text: also holds for . The case of  is controversial. In contexts where only integer powers are considered, the value  is generally assigned to  but, otherwise, the choice of whether to assign it a value and what value to assign may depend on context.
  Negative exponents
  Exponentiation with negative exponents is defined by the following identity, which holds for any integer  and nonzero :
  .
  Raising 0 to a negative exponent is undefined but, in some circumstances, it may be interpreted as infinity ().
  This definition of exponentiation with negative exponents is the only one that allows extending the identity  to negative exponents (consider the case ).
  The same definition applies to invertible elements in a multiplicative monoid, that is, an algebraic structure, with an associative multiplication and a multiplicative identity denoted  (for example, the square matrices of a given dimension). In particular, in such a structure, the inverse of an invertible element  is standardly denoted
  Identities and properties
  The following identities, often called , hold for all integer exponents, provided that the base is non-zero:
  Unlike addition and multiplication, exponentiation is not commutative. For example, . Also unlike addition and multiplication, exponentiation is not associative. For example, , whereas . Without parentheses, the conventional order of operations for serial exponentiation in superscript notation is top-down (or right-associative), not bottom-up (or left-associative). That is,
  which, in general, is different from