Exponentiation

In mathematics, exponentiation, denoted b, is an operation involving two numbers: the base, b, and the exponent, n. When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, b is the product of multiplying b by itself n times: $${\displaystyle b^{n}=\underbrace {b\times b\times \dots \times b\times b} _{n{\text{ times}}}.}$$

The definition of exponentiation can be extended in a natural way to define ${\displaystyle b^{x}}$ for any positive real number base ${\displaystyle b}$ and any real number exponent ${\displaystyle x}$. A more involved definition supports arbitrary complex numbers as base and exponent. Other generalizations allow algebraic objects, such as square matrices, to be the base.

Exponentiation is a fundamental operation used throughout mathematics, science, and engineering.