If your space constraints are not strict, like two column typesetting, you can use \medmath
from the nccmath
package: this reduces ambiguities in the formula.
\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{nccmath}
\begin{document}
\begin{equation*}
\phi_{i} = x_{i}+\sum_{k\neq i}x_{k}
\medmath{
\frac{\displaystyle
\frac{5}{3}\frac{1}{A_{ik}^{*}}+\frac{M_{k}}{M_{i}}
}{\displaystyle
1+\frac{M_k\mathstrut}{M_i}
}
\,
\frac{\displaystyle
\Bigl(
F_{ik}+B_{ik}\sqrt{\frac{\eta_i}{\eta_k}}
\Bigl(\frac{M_{k}}{M_{i}}\Bigr)^{1/4}
\Bigr)^2
}{\displaystyle
\sqrt{8\left(1+\frac{M_i}{M_k}\right)}
}
}% end of \medmath
\end{equation*}
\end{document}

Actually, a comparison with the slashed version shows the space is less with the above version.
\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{nccmath}
\begin{document}
\begin{equation*}
\begin{split}
\phi_{i} ={}& x_{i}+\sum_{k\neq i}x_{k}
\biggl[
\frac{5}{3}\frac{1}{A_{ik}^{*}}+\frac{M_{k}}{M_{i}}
\biggr]
\bigg/
\biggl[
1+\frac{M_k}{M_i}
\biggr]
\\
&\times
\biggl[
F_{ik}+B_{ik}\sqrt{\frac{\eta_i}{\eta_k}}\left(\frac{M_{k}}{M_{i}}\right)^{\!1/4}
\biggr]^2
\bigg/
\biggl[
\sqrt{8\left(1+\frac{M_i}{M_k}\right)}
\biggr]
\end{split}
\end{equation*}
\begin{equation*}
\phi_{i} = x_{i}+\sum_{k\neq i}x_{k}
\medmath{
\frac{\displaystyle
\frac{5}{3}\frac{1}{A_{ik}^{*}}+\frac{M_{k}}{M_{i}}
}{\displaystyle
1+\frac{M_k\mathstrut}{M_i}
}
\,
\frac{\displaystyle
\Bigl(
F_{ik}+B_{ik}\sqrt{\frac{\eta_i}{\eta_k}}
\Bigl(\frac{M_{k}}{M_{i}}\Bigr)^{1/4}
\Bigr)^2
}{\displaystyle
\sqrt{8\left(1+\frac{M_i}{M_k}\right)}
}
}% end of \medmath
\end{equation*}
\end{document}

You can judge what's the clearer way to display your formula.