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  2. Base (exponentiation) - Wikipedia

    en.wikipedia.org/wiki/Base_(exponentiation)

    The number n is called the exponent and the expression is known formally as exponentiation of b by n or the exponential of n with base b. It is more commonly expressed as "the nth power of b", "b to the nth power" or "b to the power n". For example, the fourth power of 10 is 10,000 because 10 4 = 10 × 10 × 10 × 10 = 10,000.

  3. Reciprocal rule - Wikipedia

    en.wikipedia.org/wiki/Reciprocal_rule

    In calculus, the reciprocal rule gives the derivative of the reciprocal of a function f in terms of the derivative of f.The reciprocal rule can be used to show that the power rule holds for negative exponents if it has already been established for positive exponents.

  4. 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 ...

  5. Modular exponentiation - Wikipedia

    en.wikipedia.org/wiki/Modular_exponentiation

    Inputs An integer b (base), integer e (exponent), and a positive integer m (modulus) Outputs The modular exponent c where c = b e mod m. Initialise c = 1 and loop variable e′ = 0; While e′ < e do Increment e′ by 1; Calculate c = (b ⋅ c) mod m; Output c; Note that at the end of every iteration through the loop, the equation c ≡ b e ...

  6. Fourth power - Wikipedia

    en.wikipedia.org/wiki/Fourth_power

    In arithmetic and algebra, the fourth power of a number n is the result of multiplying four instances of n together. So: n 4 = n × n × n × n. Fourth powers are also formed by multiplying a number by its cube. Furthermore, they are squares of squares.

  7. Ordinal arithmetic - Wikipedia

    en.wikipedia.org/wiki/Ordinal_arithmetic

    The definition of exponentiation can also be given by transfinite recursion on the exponent β. When the exponent β = 0, ordinary exponentiation gives α 0 = 1 for any α. For β > 0, the value of α β is the smallest ordinal greater than or equal to α δ · α for all δ < β. Writing the successor and limit ordinals cases separately: α 0 = 1.

  8. Gasoline Linked to 150 Million Cases of Mental Health ...

    www.aol.com/lifestyle/gasoline-linked-150...

    A new study says that exhaust from gasoline containing lead may have contributed to ADHD, anxiety, and other mental health disorders in a large segment of the population

  9. Stretched exponential function - Wikipedia

    en.wikipedia.org/wiki/Stretched_exponential_function

    With a stretching exponent β between 0 and 1, the graph of log f versus t is characteristically stretched, hence the name of the function. The compressed exponential function (with β > 1) has less practical importance, with the notable exception of β = 2, which gives the normal distribution.

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