Variable or constant raised to power {exponent, arithmetic} indicates to multiply power number of times. For example, 2^4 = 2*2*2*2. Fractional exponents are roots. For example, square root has exponent 0.5: 4^0.5 = 2.
Constant or variable can have power {involution, mathematics}.
Constant or variable can have nth root {evolution, mathematics}.
Bases can have exponent zero {zeroth power}: x^0. Bases, except zero, to zeroth power equal one: x^0 = 1 and 2^0 = 1. Zero to zeroth power has no definition: 0^0 = null.
Exponents {fractional exponent} can be fractions. If exponent is 1/2, find square root. If exponent is 1/3, find cube root. If exponent is 1/n, where n is integer, find nth root. Exponentials with fractional exponents, of form 1/n, have main roots {principal nth root}.
Fractional exponent can have special root symbol {radical sign}, with fraction denominator placed in crook of radical sign.
Fractional exponent can have the base {radicand}, raised to fraction numerator, inside radical sign.
Powers {logarithm, exponential} of bases make numbers. For number e^2, ln(e^2) = 2. For number 100, log(100) = log(10^2) = 2. Taking logarithms and finding exponentials are inverses.
Logarithms {Naperian logarithm} can use base 10. For example, log(100) = 2, because 10^2 = 100.
Logarithms {natural logarithm, exponential}| {hyperbolic logarithm} can use base e. For example, ln(e^2) = 2.
Numbers can multiply logarithms with one base to give logarithms with another base {modulus, logarithm}.
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Date Modified: 2022.0225