section_path: Integer exponents/Powers of a sum
section_name: Powers of a sum
paragraph_text: Powers of a sum
  
  The powers of a sum can normally be computed from the powers of the summands by the binomial formula
  
  However, this formula is true only if the summands commute (i.e. that ab = ba), which is implied if they belong to a structure that is commutative. Otherwise, if a and b are, say, square matrices of the same size, this formula cannot be used. It follows that in computer algebra, many algorithms involving integer exponents must be changed when the exponentiation bases do not commute. Some general purpose computer algebra systems use a different notation (sometimes ^^ instead of ^) for exponentiation with non-commuting bases, which is then called non-commutative exponentiation.