Editing Exponentiation (section)

===Powers of a sum===
The powers of a sum can normally be computed from the powers of the summands by the [[binomial formula]]
: <math>(a+b)^n=\sum_{i=0}^n \binom{n}{i}a^ib^{n-i}=\sum_{i=0}^n \frac{n!}{i!(n-i)!}a^ib^{n-i}.</math>

However, this formula is true only if the summands commute (i.e. that {{math|1=''ab'' = ''ba''}}), which is implied if they belong to a [[algebraic structure|structure]] that is [[commutative property|commutative]]. Otherwise, if {{mvar|a}} and {{mvar|b}} are, say, [[square matrix|square matrices]] of the same size, this formula cannot be used. It follows that in [[computer algebra]], many [[algorithm]]s involving integer exponents must be changed when the exponentiation bases do not commute. Some general purpose [[computer algebra system]]s use a different notation (sometimes {{math|^^}} instead of {{math|^}}) for exponentiation with non-commuting bases, which is then called '''non-commutative exponentiation'''.