exponentiation
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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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Article
52 sectionsContents
- Etymology
- History
- 20th century
- Terminology
- Integer exponents <span class="anchor" id="Integer"></span>
- Positive exponents
- Zero exponent
- Negative exponents
- Identities and properties
- Powers of a sum
- Combinatorial interpretation
- Particular bases
- Powers of ten <span class="anchor" id="Base 10"></span>
- {{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 <span class="anchor" id="Programming"></span>
- 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.