How to fix an ugly fraction with exponent?

Question

Here's a simple fraction that I find extremely ugly. What could I do to get a better looking result (without using a negative exponent) ?

\documentclass[11pt,letterpaper,twoside]{book}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage[total={6in,10in},left=1.5in,top=0.5in,includehead,includefoot]{geometry}
\usepackage{microtype}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{mathtools}
\usepackage{tensor}

\begin{document}

TEST
\begin{equation}
    a(t) = \frac{g}{\bigl(1 + (g t / c)^2 \bigr)^{\frac{3}{2}}}.
\end{equation}

\end{document}

Preview:

Of course, I could use 3/2 instead of \frac{3}{2}, but I believe the result is worst. I tried \displaystyle and \textstyle for the bottom part of the fraction, but the exponent is still creating the trouble. So what would you do to get a better looking fraction with its pesky exponent, without writing everything at the numerator with a negative exponent?

Answer 1

A couple of suggestions

\documentclass[11pt,letterpaper,twoside]{book}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage[total={6in,10in},left=1.5in,top=0.5in,includehead,includefoot]{geometry}
\usepackage{microtype}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{mathtools}
\usepackage{tensor}

\begin{document}

TEST
\begin{equation}
    a(t) = \frac{g}{\bigl(1 + (g t / c)^2 \bigr)^{\frac{3}{2}}}.
\end{equation}

TEST2
\begin{equation}
    a(t) = \frac{g}{(1 + (g t / c)^2)^{\frac{3}{2}}}.
\end{equation}


TEST3
\begin{equation}
    a(t) = \frac{g}{(1 + (g t / c)^2)^{\scriptscriptstyle\frac{3}{2}}}.
\end{equation}

\end{document}

Answer 2

Perhaps this hack with bigstrut will befit you?

\documentclass[11pt,letterpaper,twoside]{book}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage[total={6in,10in},left=1.5in,top=0.5in,includehead,includefoot]{geometry}
\usepackage{microtype}
\usepackage{amsfonts}
\usepackage{mathtools}
\usepackage{bigstrut}
\newcommand{\mybigstrut}[1] {{\setlength{\bigstrutjot}{#1}\bigstrut[b]}}

\begin{document}

TEST

\begin{equation}
    a(t) = \frac{g_{\mybigstrut{5pt}}}{\bigl(1 + (g t / c)^2 \bigr)^{\!\frac{3}{2}}}.
\end{equation}

\end{document} 

Answer 3

One approach is to move the exponent out from the denominator and reposition it accordingly. I used \! to move it left a bit, and then either raisebox to lower it by trial and error or genfrac to have the exponent in a phantom denominator.

\documentclass[11pt]{amsart}

\begin{document}

\begin{align*}
\text{original: }&a(t) = \frac{g}{\bigl(1 + (g t / c)^2 \bigr)^{\frac{3}{2}}}.\\
\text{raisebox: }&a(t) = \frac{g}{\bigl(1 + (g t / c)^2 \bigr)}\!\raisebox{-.5ex}{$\scriptstyle\frac{3}{2}$}.\\
\text{genfrac: }&a(t) = \frac{g}{\bigl(1 + (g t / c)^2 \bigr)}\!\genfrac{}{}{0pt}{0}{}{{}^{\frac{3}{2}}}.
\end{align*}

\end{document}