exponentiation

Also known as to the power

[[File:Expo02.svg|thumb|Graphs of for various bases :

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Exponentiation is a mathematical operation where a number (called the base) is multiplied by itself a certain number of times, determined by another number (called the exponent). It matters because it's a fundamental tool used throughout mathematics, science, and everyday applications like calculating compound interest, understanding population growth, and describing how quickly things can increase or decrease.

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Commons category: Exponentiation
Stack Exchange tag: stackoverflow.com/tags/exponent

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~57 min read

Article

52 sections

Contents

Etymology
History
20th century
Terminology
Integer exponents
Positive exponents
Zero exponent
Negative exponents
Identities and properties
Powers of a sum
Combinatorial interpretation
Particular bases
Powers of ten
{{anchor|Base 2}}Powers of two
Powers of one
Powers of zero
Powers of negative one
Large exponents
Power functions
Table of powers
Rational exponents
Real exponents
Limits of rational exponents
Exponential function
Powers via logarithms
Complex exponents with a positive real base
Non-integer exponents with a complex base
{{mvar|n}}th roots of a complex number
Roots of unity
Complex exponentiation
Principal value
Multivalued function
Computation
Examples
Failure of power and logarithm identities
Irrationality and transcendence
Integer powers in algebra
In a group
In a ring
Matrices and linear operators
Finite fields
Powers of sets {{Anchor|Exponentiation over sets}}
Sets as exponents
In category theory
Repeated exponentiation
Limits of powers
Efficient computation with integer exponents
Iterated functions
In programming languages
See also
Notes
References

thumb|Graphs of for various bases :

Each curve passes through the point because any nonzero number raised to the power of is . At , the value of equals the base because any number raised to the power of is the number itself.