Exponentiation

Graphs of $y = b x$ for various bases $b$ . Each curve passes through the point $(0, 1)$ because any nonzero number raised to the power of $0$ is $1$ . At $x = 1$ , the value of $y$ equals the base because any number raised to the power of $1$ is the number itself.

Addition (+)
	$\scriptstyle \left.{\begin{matrix}\scriptstyle {\text{term}}\,+\,{\text{term}}\\\scriptstyle {\text{summand}}\,+\,{\text{summand}}\\\scriptstyle {\text{addend}}\,+\,{\text{addend}}\\\scriptstyle {\text{augend}}\,+\,{\text{addend}}\end{matrix}}\right\}\,=\,$	$\scriptstyle {\text{sum}}$
Subtraction (−)
	$\scriptstyle \left.{\begin{matrix}\scriptstyle {\text{term}}\,-\,{\text{term}}\\\scriptstyle {\text{minuend}}\,-\,{\text{subtrahend}}\end{matrix}}\right\}\,=\,$	$\scriptstyle {\text{difference}}$
Multiplication (×)
	$\scriptstyle \left.{\begin{matrix}\scriptstyle {\text{factor}}\,\times \,{\text{factor}}\\\scriptstyle {\text{multiplier}}\,\times \,{\text{multiplicand}}\end{matrix}}\right\}\,=\,$	$\scriptstyle {\text{product}}$
Division (÷)
	$\scriptstyle \left.{\begin{matrix}\scriptstyle {\frac {\scriptstyle {\text{dividend}}}{\scriptstyle {\text{divisor}}}}\\[1ex]\scriptstyle {\frac {\scriptstyle {\text{numerator}}}{\scriptstyle {\text{denominator}}}}\end{matrix}}\right\}\,=\,$	$\scriptstyle \left\{{\begin{matrix}\scriptstyle {\text{fraction}}\\\scriptstyle {\text{quotient}}\\\scriptstyle {\text{ratio}}\end{matrix}}\right.$
Exponentiation
	$\scriptstyle \left.{\begin{matrix}\scriptstyle {\text{base}}^{\text{exponent}}\\\scriptstyle {\text{base}}^{\text{power}}\end{matrix}}\right\}\,=\,$	$\scriptstyle {\text{power}}$
nth root (√)
	$\scriptstyle {\sqrt[{\text{degree}}]{\scriptstyle {\text{radicand}}}}\,=\,$	$\scriptstyle {\text{root}}$
Logarithm (log)
	$\scriptstyle \log _{\text{base}}({\text{anti-logarithm}})\,=\,$	$\scriptstyle {\text{logarithm}}$

In mathematics, exponentiation, denoted $b n$ , 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, $b n$ is the product of multiplying $b$ by itself $n$ times: $b^{n}=\underbrace {b\times b\times \dots \times b\times b} _{n{\text{ times}}}.$

The definition of exponentiation can be extended in a natural way to define $b^{x}$ for any positive real number base $b$ and any real number exponent $x$ . 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.