Do you mind something like this:

\documentclass{article}
\usepackage{mathtools,array}
% for show equation only
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{equation}
\setlength\PreviewBorder{1em}
\begin{document}
\begin{equation}
\left[\begin{tabular}{@{}>{$}c<{$}@{}}
\dfrac{\left(\vec{A} - \dfrac{b}{c}\vec{D}\right)}{E^2}
\end{tabular}\right]^{1/2}
\end{equation}
\end{document}
Addendum: More simple code is, if instead of tabular the environment array is used:
\begin{equation}
\left[\begin{array}{@{} c @{}
}
\dfrac{\left(\vec{A} - \dfrac{b}{c}\vec{D}\right)}{E^2}
\end{array}\right]^{1/2}
\end{equation}
Result is the same ase before.
\displaystylein the middle of an expression. If you must use it then it should almost always be at the start. – David Carlisle Feb 12 '16 at 21:17