Editing Exponentiation (section)

===Negative exponents===
Exponentiation with negative exponents is defined by the following identity, which holds for any integer {{mvar|n}} and nonzero {{mvar|b}}:
: <math>b^{-n} = \frac{1}{b^n}</math>.<ref name=":1"/>
Raising 0 to a negative exponent is undefined but, in some circumstances, it may be interpreted as infinity (<math>\infty</math>).<ref>{{cite book
 | last = Knobloch | first = Eberhard | author-link = Eberhard Knobloch
 | editor1 = Kostas Gavroglu |editor2=Jean Christianidis |editor3=Efthymios Nicolaidis
 | contribution = The infinite in Leibniz’s mathematics – The historiographical method of comprehension in context
 | doi = 10.1007/978-94-017-3596-4_20
 | isbn = 9789401735964
 | publisher = Springer Netherlands
 | series = Boston Studies in the Philosophy of Science
 | title = Trends in the Historiography of Science
 | year = 1994
 | volume = 151 |page = 276
 |quote=A positive power of zero is infinitely small, a negative power of zero is infinite.}}</ref>

This definition of exponentiation with negative exponents is the only one that allows extending the identity <math>b^{m+n}=b^m\cdot b^n</math> to negative exponents (consider the case <math>m=-n</math>).

The same definition applies to [[invertible element]]s in a multiplicative [[monoid]], that is, an [[algebraic structure]], with an associative multiplication and a [[multiplicative identity]] denoted {{math|1}} (for example, the [[square matrix|square matrices]] of a given dimension). In particular, in such a structure, the inverse of an [[invertible element]] {{mvar|x}} is standardly denoted <math>x^{-1}.</math>