Why is exponent so low when used with hat-quantity in a fraction? Is this a bug?

Question

Here is the MWE:

\documentclass{article}
\begin{document}
\[
\hat{R}^2\quad\frac{1}{\hat{R}^2}
\]
\end{document}

which give (I highlight with red for better see the lower "2" in the second expression):

Answer 1

Just to follow-up on @DavidCarlisle's answer: One can undo cramped-textstyle mode in the denominator of a \dfrac expression by issuing the directive \textstyle. Conversely, one can force cramped displaystyle by loading the mathtools package and making use of its \cramped macro.

\documentclass{article}
\usepackage{mathtools}  % for 'cramped' macro
\begin{document}
\[
R^2 \quad                     % uncramped displaystyle
\cramped{R^2} \quad           % cramped   displaystyle
\frac{1}{R^2 R^2} \quad       % cramped   textstyle
\frac{1}{\textstyle R^2 R^2}  % uncramped textstyle
\]
\end{document}

If you look really closely, you'll notice that the exponent isn't set quite as high in uncramped textstyle math mode as it is in uncramped displaystyle math mode.

Answer 2

Not really a bug just a perhaps unfortunate combination of features.

\documentclass{article}
\begin{document}
\[
\hat{R}^2R^2\quad\frac{1}{\hat{R}^2 R^2}\quad\frac{1}{R^2 R^2}
\]
\end{document}

The superscript on the accented base is positioned to match that on an unaccented base, not raised higher.

denominators are set in "cramped mode" to avoid opening up the fraction.

But with the accented R the fraction is opened up in any case.

This behaviour is really set in the tex core layout rules and the font parameters of the font being used, not directly by LaTeX.