Exponentiation

Exponentiation raises a base to a power. For positive integer exponents, it multiplies the base by itself the indicated number of times; extensions cover zero, negative, fractional, and complex exponents.

Exponent laws: Identities governing products, quotients, and powers with exponents. These rules simplify expressions such as products of powers with the same base.
Base (exponentiation): The number or expression raised to a power. The base is the quantity repeated in integer-power multiplication.
Exponential function: A function in which a fixed positive base is raised to a variable exponent. It turns exponentiation into a continuous model of changing quantities.
Tetration: An operation that iterates exponentiation, forming a power tower. It extends exponentiation by repeating the operation itself.
Negative exponent: An exponent below zero, defined for nonzero bases by taking the reciprocal of the corresponding positive power. Reciprocals extend exponentiation from positive to negative integer powers.
Exponent: A number indicating a power to which a base is raised. The exponent specifies the operation’s power and its extensions.
Exponential growth: Growth at a rate proportional to the quantity already present. Repeated proportional increases produce powers and exponential curves.
Factorial: The product of all positive integers up to a given nonnegative integer. Factorials grow rapidly too, but multiply consecutive integers rather than repeating one base.
Rational exponent: An exponent expressible as a ratio of integers, commonly interpreted through roots and integer powers. Fractional powers connect exponentiation to root extraction.
Multiplication: An arithmetic operation combining quantities through repeated addition or scaling. Positive integer exponentiation is repeated multiplication.

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