\documentclass[12pt]{article}
\pagestyle{empty}
\begin{document}
\begin{displaymath}
P_{\rm select}({\bf r}_i) = 
{{
\left[
{{p_{\rm trial}^{\rm ideal}({\bf r}_i)}\over{ p_{\rm trial}^{\rm arb}({\bf r}_i)}}
w_{\rm bias}({{\bf r}_i},{\bf r}_{\rm exist})
\exp\left[-\beta u({\bf r}_i)\right]
\right]
}
\over
{
W_k
}}
\end{displaymath}
\end{document}