Is there a more correct way to show explicit exponential operators?

Question

I typed in this question like this:

$\underbrace{\alpha \hat{\phantom{\hat{}}} \alpha \hat{\phantom{\hat{}}} \dots \hat{\phantom{\hat{}}} \alpha}_\text{n times}$

which mathjax prints as

I feel there should be a more correct way to do this.

Answer 1

You could also type

\def\mhat{\mathbin{\hat{\vphantom{x}}}} % spacing like a binary operator 
$\underbrace{\alpha\mhat\alpha\mhat\cdots\mhat\alpha}_{\text{$n$ times}}$

Answer 2

There doesn't seem to be a circumflex (hat) symbol intended for use in maths mode, except as an accent. However, you can use the text mode version \textasciicircum (or alternatively just \^{}). This avoids the need for phantoms.

\documentclass{article}
\usepackage{amsmath}
\newcommand\mathcirc{\text{\textasciicircum}}
\begin{document}
\[
\underbrace{\alpha \mathcirc \alpha \mathcirc  \ldots \mathcirc \alpha}_{n\text{ times}}
\]
\end{document}

Answer 3

Perhaps you might like to use

\newcommand\expon{\mathbin {^\wedge}}

or, if you're quite flexible about the symbol you use, adopt Knuth's up-arrow notation:

\newcommand\expon {\mathbin {\uparrow}}

Answer 4

A variant without hat that counts the exponential operations:

$\bigl(\bigl(\bigl(\alpha
\underbrace{
  ^\alpha\bigr)^\alpha\bigr)^{\cdots}\bigr)^\alpha
}_\text{$n$ times}
= \alpha^{(\alpha^n)}$

Answer 5

Just like Heiko's answer, but without the parentheses:

\alpha
\underbrace{
  {{{^{\alpha\vphantom{h}}}^{\alpha\vphantom{h}}}^{\cdots\vphantom{h}}}^{\alpha\vphantom{h}}
}_{\text{$n$ times}}
= \alpha^{(\alpha^n)}

(A \strut instead of \vphantom{h} gives me too much vertical space.)

(Probably better with \! after the initial \alpha.)