2014年3月8日 · 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 …

2014年10月3日 · 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 …

2012年9月5日 · Over the reals, the concept that "exponentiation = repeated multiplication" breaks down when you have non-integer exponents, so you have to start defining exponentiation …

The short answer is "take logs". The logarithm, or log, of a number reflects what power you need to raise a certain base to in order to get that number.

$\begingroup$ I disagree, you can actually write any decimal as a fraction. 0.14 is fourteen hundredths, or simplified 7/50. then add in 2/1 by raising to lowest common denominator, you …

With quite a lot of effort, we can then show that the familiar laws of exponentiation hold. The above approach, though intuitively very natural, is unwieldy. So in practice, we usually take …

If you are serious about "as simple as possible" then observe that $27^{41} = 3^{123}$ and use Carmichael's theorem (a strengthening of Euler's theorem which actually gives a tight bound) …

While this would make things more convenient for us, exponentiation, unfortunately, does not work like this. For example: $(1+1)^2 = 4$ but $1^2 + 1^2 = 2$. Recall that, for multiplication, it …

2015年2月3日 · I was wondering, what is the order of operations when it comes to multi level exponents. Couldn't find anything in google.

2016年10月7日 · That is why a lot of definitions need to be justified by theorems. In this case we extend the old structure (reals with integer exponentiation) to a new one (reals with rational …