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Mar 8, 2014 · Exponentiation is a correspondence between addition and multiplication. Think of a number line, with $0$ in the "middle", and tick marks at each integer. Moving a certain distance to the right correspond...
Dec 18, 2023 · I was wondering why addition has one inverse (subtraction), multiplication has one inverse (division), but exponentiation has two (radication and logarithm). After a bit of thinking, I thought it m...
May 27, 2024 · I was taught my whole life that if I want to get rid of a root I should just do the inverse and ''exponentiate that with its index'' and now I just learn that roots aren't the inverse of exponentiation ...
23 Some tricks which are useful for modular exponentiation The intention of this post is to collect various tricks which can sometimes simplify computations of this type. (Especially when done by hand and not using co...
May 21, 2018 · When rigorously laying out foundations of all of analysis, the usual method is to use the definition $$ a^b = \exp (b \log (a)) $$ While you could try and define exponentiation directly, it is somewhat ...
Mar 13, 2012 · Modular exponentiation by repeated squaring (and peasant multiplication] Ask Question Asked 14 years ago Modified 11 months ago
Oct 3, 2015 · Over the reals, the concept that "exponentiation = repeated multiplication" breaks down when you have non-integer exponents, so you have to start defining exponentiation using suprema of sets, which expl...
Nov 3, 2017 · Rather than trying to press complex exponentiation into the mold of repeated multiplication, see complex exponentiation -- or more fundamentally, the function $\exp$ -- as its own thing, that in special ...
Oct 3, 2024 · We can write $3^ {0.6}$ as $3^\frac6 {10}$ and can be simplified to $3^\frac3 {5}$, yet it is tedious to calculate by hand, as well as $3^e$ and $3^ {\pi}$? How can I do this without calculator? Like h...
Sep 6, 2024 · I have been trying to rigorously define real exponentiation. Online there doesn't seem to be ANY definition of real exponentiation that covers every case of base and exponent. In school and on non-
