Minus sign not aligning with fraction

Question

When I use subscripts and superscript with \frac the numerator and denominator looks very tight,

\documentclass[a4paper,12pt]{article}
\usepackage{mathtools,amssymb}
\begin{document}
[e^{-\frac{(x-\mu_2)^2}{2\sigma^2_2}}]
[e^{-\dfrac{(x-\mu_2)^2}{2\sigma^2_2}}]
\end{document}

So I tried using \dfrac but not the minus sign and fraction line are not aligned.

Anybody has a smart fix to this?

Answer 1

The cause of the misalignment is that the minus sign is in scriptstyle, but the fraction is being forced into displaystyle. Here are a few options:

\[e^{\displaystyle -\frac{(x-\mu_2)^2}{2\sigma^2_2}}\]

\[e^{\dfrac{-(x-\mu_2)^2}{2\sigma^2_2}}\]

\[e^{-(x-\mu_2)^2/2\sigma^2_2}\]

\[\exp\bigl(-(x-\mu_2)^2/2\sigma^2_2\bigr)\]

Answer 2

Let's consider five separate typographic approaches to displaying the expression at hand:

• e^{-\dfrac{(...)}{...}} and e^{\dfrac{-(...)}{...}}

• e^{-\tfrac{(...)}{...}} and e^{\tfrac{-(...)}{...}}

• e^{-(x-\mu_2)^2/(2\sigma_2^2)} (inline-style fraction in exponent)

• \exp(-\dfrac{...}{...}) and \exp(-\tfrac{...}{...})

• \exp\bigl(-(x-\mu_2)^2/(2\sigma_2^2)\bigr) (inline-style fraction)

I think we may posit that the expressions in the first two rows look awful. (Ok, row 1 is truly awful, whereas row 2 is just plain awful.) If you must use e^{...} notation, then do please consider using the inline-fraction variant in row 3. That said, I'd really, really recommend that you consider adopting \exp(...) notation; cf. rows 4 and 5.

\documentclass{article} % or some other suitable document class
\usepackage{amsmath} % for 'gather*' env.
\begin{document}
\begin{gather*}
e^{-\dfrac{(x-\mu_2)^2}{2\sigma_2^2}} \qquad
e^{\dfrac{-(x-\mu_2)^2}{2\sigma_2^2}} \\[\jot]
e^{-\tfrac{(x-\mu_2)^2}{2\sigma_2^2}} \qquad
e^{\tfrac{-(x-\mu_2)^2}{2\sigma_2^2}} \\[\jot]
e^{-(x-\mu_2)^2/(2\sigma_2^2)}        \\[\jot]
\exp\biggl(-\frac{(x-\mu_2)^2}{2\sigma_2^2}\biggr) \qquad
\exp\Bigl(-\tfrac{(x-\mu_2)^2}{2\sigma_2^2}\Bigr) \\[\jot]
\exp\bigl(-(x-\mu_2)^2/(2\sigma_2^2)\bigr)
\end{gather*}
\end{document}

Answer 3

If you want necessarily to use \dfrac with the minus sign you add \ooalign.

\documentclass[a4paper,12pt]{article}
\usepackage{mathtools,amssymb}
\begin{document}
\[e^{-\frac{(x-\mu_2)^2}{2\sigma^2_2}}\]
\[e^{\ooalign{$-$}\dfrac{(x-\mu_2)^2}{2\sigma^2_2}}\]
\end{document}

Addendum: Using the comment of @campa with \hbox you obtain the same result.

\documentclass[a4paper,12pt]{article}
\usepackage{mathtools,amssymb}
\begin{document}
\[e^{-\frac{(x-\mu_2)^2}{2\sigma^2_2}}\]
\[e^{\hbox{$-$}\dfrac{(x-\mu_2)^2}{2\sigma^2_2}}\]
\end{document}

Update 2022-04-14

Based on the discussions from this question, I propose to use \mbox instead of \hbox.

The main difference is that using \hbox in LaTeX can lead to unexpected results. So always use the latter, unless you know what you're doing with \hbox. -- egreg

\documentclass[a4paper,12pt]{article}
\usepackage{mathtools,amssymb}
\begin{document}
default: \[e^{-\frac{(x-\mu_2)^2}{2\sigma^2_2}}\]
hbox: \[e^{\hbox{$-$}\dfrac{(x-\mu_2)^2}{2\sigma^2_2}}\]
mbox: \[e^{\mbox{$-$}\dfrac{(x-\mu_2)^2}{2\sigma^2_2}}\]
\end{document}