Resize/Scale equation in Beamer

Instead of keeping the small (normal) font size and scaling the equation to make it bigger, I would use a font command for it. If you simply use \Huge at the beginning of your center environment, you will get:

I used the demo option to get a black rectangle, because I did not have your picture. And I defined some \e. Besides that, the change was here:

\begin{center}
    \Huge
    $F = a \cdot x^b + c \cdot sign(\dot x) \cdot x^d \cdot
    |\dot x|^e$
\end{center}

Since \Huge has been used within an environment, the font size change is local to that. Instead of centering inline math, I would use displayed math, which is automatically centered:

{\Huge
  \[
    F = a \cdot x^b + c \cdot sign(\dot x) \cdot x^d \cdot|\dot x|^e
  \]}

Use \scalebox or \resizebox from the graphicx package:

\documentclass{beamer}
\usepackage{graphicx}% http;//ctan.org/pkg/graphicx
\begin{document}
\begin{frame}
\begin{columns}
\column{0.6\textwidth}
    \includegraphics[width=6cm]{FvsD.png}
    \column{0.4\textwidth}
    \begin{minipage}[c][.5\textheight][c]{\linewidth}
    \begin{itemize}
        \item[]<1> $a = 2.35\e{6}$ \\
        \item[]<1> $b = 1.72$ \\
        \item[]<1> $c = 2.00\e{4}$ \\
        \item[]<1> $d = 0.91$ \\
        \item[]<1> $e = 1.00$
    \end{itemize}
    \end{minipage}
\end{columns}
\begin{center}
  \scalebox{2}{%
    $F = a \cdot x^b + c \cdot sign(\dot x) \cdot x^d \cdot | \dot x|^e$%
  }
\end{center}
\end{frame}
\end{document}

\scalebox{<factor>}{<stuff>} scales <stuff> by a factor of <factor>, while \resizebox{<width>}{<height>}{<stuff>} does the same in terms of the lengths (or dimensions) <width> and <height>. If aspect ratio should be maintained, specify only one length and make the other !.