Exponentiation

In mathematics, exponentiation, denoted bn, 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, bn is the product of multiplying b by itself n times: b n = b × b × ⋯ × b × b ⏟ 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 b x {\displaystyle b^{x}} for any positive real number base b {\displaystyle b} and any real number exponent x {\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.