Lowering the height of a superscript?

If you load the amsmath package, \hat{\bar{M}}^{a} will not only give you the desired, i.e., smaller height offset for the exponent term automatically, it'll also stack the "hat" and "bar" accent symbols in a much more pleasing way.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
$\hat{\bar{M}}^{a}$
\end{document}

Like this?

\documentclass[margin=3mm]{standalone}

\begin{document}
$\hat{\bar{M}}{}^{a}$ $\hat{\bar{M}}^{a}$
\end{document}

See, if use of \widehat instead of \hat gives more appealing result.