Exponentiation
When it is a positive integer, the exponent indicates how many copies of the base are multiplied together. For example, . The base appears times in the repeated multiplication, because the exponent is . Here, is the "base", is the "exponent", and is the "power" or, more specifically, "3 raised to the 5th power".
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.