Exponentiation
Exponentiation is a mathematical operation, written as , involving two numbers, the "base" and the "exponent" . When is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, is the product of multiplying bases:
Logarithm
Exponentiation may be extended to , where is a positive number and the "exponent" is any real number. For example, is the reciprocal of , that is, . Raising "b" to the power 1/2 is the square root of "b". More generally, raising "b" to a rational power "p"/"q", where "p" and "q" are integers, is given by
the "q"-th root of "b". Finally, any irrational number (a real number which is not rational) "y" can be approximated to arbitrary precision by rational numbers. This can be used to compute the "y"-th power of "b": for example formula_9 and formula_10 is increasingly well approximated by formula_11. A more detailed explanation, as well as the formula is contained in the article on exponentiation.