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\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsfonts}

\thispagestyle{empty}
\begin{document}
\begin{equation}
  S(r)=S_{0,1}(1+\frac{r^2}{r_{c,1}^2})^{-3\beta_1+1/2}+S_{0,2}(1+\frac{r^2}{r_{c,2}^2})^{-3\beta_2+1/2}\notag
\end{equation}
\end{document}