# Formatting a fractional exponent in display math

Typographically, what is the correct way to display a fractional exponent in display math mode? There was a post regarding inline math, but consider this example.

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}

\begin{document}

\begin{equation*}
\left( \frac{1}{t}\right)^{3/2} x
\end{equation*}

\end{document}


The spacing becomes especially pronounced if a partial derivative follows, for example:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}

\begin{document}

\begin{equation*}
\left( \frac{1}{t}\right)^{3/2} \frac{\partial}{\partial x}\sqrt{\frac{1}{x}}
\end{equation*}

\end{document}


Should one use the \frac{}{} function for fractional exponents at all? Or is it better to just use x^2/4t instead?

• The output generated by the expression \frac{1}{t}^{3/2} is ambiguous: Does the exponent ("3/2") apply to the entire fraction, or just to the numerator? Either add some parentheses, or write t^{-3/2}. – Mico Jul 11 '15 at 3:48
• @Mico I edited the code accordingly. Thanks for all your help today. – Jun-Goo Kwak Jul 11 '15 at 3:49
• In your quest to master the writing of mathematics, I strongly recommend you go to this site ftp.ams.org/pub/author-info/documentation/howto/mit-2.pdf  Mathematics into Type by Swanson and study the pdf for the reference you were given by Gonzalo Medina in the preceding question tex.stackexchange.com/questions/254785/e-vs-exp-in-display-mode. – R. Schumacher Jul 11 '15 at 4:10
• @R.Schumacher Thank you for providing access to that reference. – Jun-Goo Kwak Jul 11 '15 at 4:14

What's better from a typographic point of view -- inline-style fractions or display-style fractions while in display-math mode -- depends crucially on the contents of the fractional terms.

For the two examples at hand, I can see nothing wrong with using inline-math notation, shown on the right-hand side of the two rows below.

Incidentally, I'd say that \left( \frac{1}{t}\right)^{3/2} is less than perfect, typographically speaking, not because of the presence of the fractional term \frac{1}{t} but because there's too much whitespace between \left( \frac{1}{t}\right) and the exponent (3/2). If you must use these large round parentheses, you should probably write

\left( \frac{1}{t}\right)^{\!3/2}


i.e., insert a negative thinspace before 3/2, in order to "snug up" the exponent material to the closing parenthesis.

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\begin{document}
\begin{align*}
\left( \frac{1}{t}\right)^{3/2}
&\text{ vs.\ }
t^{-3/2} \\
\frac{\partial}{\partial x}\sqrt{\frac{1}{x}}
&\text{ vs.\ }
\frac{\partial}{\partial x} x^{-1/2}
\end{align*}
\end{document}