Editing Exponentiation (section)

===Identities and properties===
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The following [[identity (mathematics)|identities]], often called '''{{vanchor|exponent rules}}''', hold for all integer exponents, provided that the base is non-zero:<ref name=":1"/>
: <math>\begin{align}
           b^m \cdot b^n &= b^{m + n} \\
  \left(b^m\right)^n &= b^{m \cdot n} \\
       b^n \cdot c^n &= (b \cdot c)^n
\end{align}</math>

Unlike addition and multiplication, exponentiation is not [[commutative]]: for example, <math>2^3 = 8</math>, but reversing the operands gives the different value <math>3^2=9</math>. Also unlike addition and multiplication, exponentiation is not [[associative]]: for example, {{math|1=(2<sup>3</sup>)<sup>2</sup> = 8<sup>2</sup> = 64}}, whereas {{math|1=2<sup>(3<sup>2</sup>)</sup> = 2<sup>9</sup> = 512}}. Without parentheses, the conventional [[order of operations]] for [[serial exponentiation]] in superscript notation is top-down (or ''right''-associative), not bottom-up<ref name="Bronstein_1987"/><ref name="NIST_2010"/><ref name="Zeidler_2013"/> (or ''left''-associative). That is,
: <math>b^{p^q} = b^{\left(p^q\right)},</math>
which, in general, is different from
: <math>\left(b^p\right)^q = b^{p q} .</math>