Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I started wondering about this the other day. Since the following have their own alternate representations. $$\begin{align*} \displaystyle\large x+x=2x & \ \frac{x}{x}=1 & xx=x^2\end{align*}$$

Can $x^x$ be represented in some other way? Thanks.

share|cite|improve this question
It could be written in many different ways algebraically. for example $x^x=\sqrt{x^{2x}}$ – NoChance Oct 7 '12 at 1:17
$x/x=1$ is not true when $x=0$, careful. – Pedro Tamaroff Oct 7 '12 at 1:17
up vote 15 down vote accepted

Yes, it's called tetration. We can write $x^x$ as $^{2}x$.

There's actually a whole chain of these iterated operators, such as the (rather) famous Knuth up-arrow notation. The page I linked to has quite a few examples if you are interested.

share|cite|improve this answer


This is a nice way to represent it if you want to differentiate it, since you can then just apply the standard differentiation rules.

Something like $$x^{x^x}$$ will be represented as $$e^{e^{x\log(x)}\log(x)}$$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.