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 ), which is implied if they belong to a structure that is commutative. Otherwise, if  and  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.
  Combinatorial interpretation
  For nonnegative integers  and , the value of  is the number of functions from a set of  elements to a set of  elements (see cardinal exponentiation). Such functions can be represented as -tuples from an -element set (or as -letter words from an -letter alphabet). Some examples for particular values of  and  are given in the following table:
  Particular bases
  Powers of ten
  In the base ten (decimal) number system, integer powers of  are written as the digit  followed or preceded by a number of zeroes determined by the sign and magnitude of the exponent. For example,  and .