exponentiation

Exponentiation is the arithmetical operation of multiplying a number times itself a given number of times. The given number is called the exponent and the number being multiplied times itself is called the base. This is typically denoted by \(a^n\), where \(a\) is the base and \(n\) is the exponent. It is common to refer to this operation by saying that we are raising \(a\) to the power \(n\).

For example, \(2^3=2\times 2\times 2 = 8\), and \(3^2=3\times 3 = 9\).

In general:

\[a^n = \underbrace{\,a \times a \times \cdots \times a\,\,}_{\text{$n$ factors}}\]

Exponentiation is the third fundamental arithmetic operation, following addition and multiplication, and preceding tetration.

It is also possible to exponentiate by powers that are negative, rational, irrational, or complex. See the article on laws of exponents for how to do this.