What Is Exponentiation? - Mathematics Stack Exchange
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 …
Why roots aren't the inverse of exponentiation but logarithms?
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 …
Why does exponentiation have 2 inverses? - Mathematics Stack Exchange
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 …
How is the definition for exponentiation extended to rationals and ...
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 …
Modular exponentiation by hand ($a^b\\bmod c$)
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 …
elementary number theory - Modular exponentiation by repeated …
Mar 13, 2012 · Modular exponentiation by repeated squaring (and peasant multiplication] Ask Question Asked 14 years, 1 month ago Modified 11 months ago
Prove that $i^i$ is a real number - Mathematics Stack Exchange
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 …
exponentiation - How can I intuitively understand complex exponents ...
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 …
exponential function - How to construct real exponentiation ...
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 …
exponentiation - What's the inverse operation of exponents ...
Oct 3, 2014 · You know, like addition is the inverse operation of subtraction, vice versa, multiplication is the inverse of division, vice versa , square is the inverse of square root, vice versa. What's the in...