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  2. Exponentiation - Wikipedia

    en.wikipedia.org/wiki/Exponentiation

    This definition of exponentiation with negative exponents is the only one that allows extending the identity + = to negative exponents (consider the case =). The same definition applies to invertible elements in a multiplicative monoid , that is, an algebraic structure , with an associative multiplication and a multiplicative identity denoted 1 ...

  3. Sums of powers - Wikipedia

    en.wikipedia.org/wiki/Sums_of_powers

    In mathematics and statistics, sums of powers occur in a number of contexts: . Sums of squares arise in many contexts. For example, in geometry, the Pythagorean theorem involves the sum of two squares; in number theory, there are Legendre's three-square theorem and Jacobi's four-square theorem; and in statistics, the analysis of variance involves summing the squares of quantities.

  4. Exponentiation by squaring - Wikipedia

    en.wikipedia.org/wiki/Exponentiation_by_squaring

    If the exponent n is zero then the answer is 1. If the exponent is negative then we can reuse the previous formula by rewriting the value using a positive exponent. That is, = (). Together, these may be implemented directly as the following recursive algorithm:

  5. Exponential function - Wikipedia

    en.wikipedia.org/wiki/Exponential_function

    Exponential functions with bases 2 and 1/2. In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative equal to its value. . The exponential of a variable ⁠ ⁠ is denoted ⁠ ⁡ ⁠ or ⁠ ⁠, with the two notations used interchangeab

  6. Power of two - Wikipedia

    en.wikipedia.org/wiki/Power_of_two

    By comparison, powers of two with negative exponents are fractions: for positive integer n, 2-n is one half multiplied by itself n times. Thus the first few negative powers of 2 are ⁠ 1 / 2 ⁠, ⁠ 1 / 4 ⁠, ⁠ 1 / 8 ⁠, ⁠ 1 / 16 ⁠, etc. Sometimes these are called inverse powers of two because each is the multiplicative inverse of a ...

  7. Laws of exponents - Wikipedia

    en.wikipedia.org/wiki/Laws_of_exponents

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  8. Arithmetic - Wikipedia

    en.wikipedia.org/wiki/Arithmetic

    Exponentiation is an arithmetic operation in which a number, known as the base, is raised to the power of another number, known as the exponent. The result of this operation is called the power. Exponentiation is sometimes expressed using the symbol ^ but the more common way is to write the exponent in superscript right after the

  9. Algebraic operation - Wikipedia

    en.wikipedia.org/wiki/Algebraic_operation

    In plain text, the TeX mark-up language, and some programming languages such as MATLAB and Julia, the caret symbol, ^, represents exponents, so x 2 is written as x ^ 2. [ 8 ] [ 9 ] In programming languages such as Ada , [ 10 ] Fortran , [ 11 ] Perl , [ 12 ] Python [ 13 ] and Ruby , [ 14 ] a double asterisk is used, so x 2 is written as x ** 2.

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