Formatting a fractional exponent in display math

Question

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?

Answer 1

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}