section_path: Integer exponents/Negative exponents
section_name: Negative exponents
paragraph_text: Negative exponents
  
  Exponentiation with negative exponents is defined by the following identity, which holds for any integer n and nonzero b:
  
  Raising 0 to a negative exponent is undefined but, in some circumstances, it may be interpreted as infinity (∞ {\displaystyle \infty }).
  
  This definition of exponentiation with negative exponents is the only one that allows extending the identity b m + n = b m ⋅ b n {\displaystyle b^{m+n}=b^{m}\cdot b^{n}} to negative exponents (consider the case m = − n {\displaystyle m=-n}).
  
  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 1 (for example, the square matrices of a given dimension). In particular, in such a structure, the inverse of an invertible element x is standardly denoted x − 1. {\displaystyle x^{-1}.}