Dashed version of \boxed

You can use the small dashbox package:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{dashbox}
\newcommand\dboxed[1]{\dbox{\ensuremath{#1}}}

\begin{document}

 \[ \dboxed{t\cdot u}\iff\dboxed{t} * \dboxed{u}\]%

\end{document} 

A possibility with tcolorbox (Description below)

\documentclass{article}

\usepackage[most]{tcolorbox}


\begin{document}
\tcbox[colback=white,boxrule=0pt,enhanced jigsaw,borderline horizontal={1pt}{0pt}{dashed},borderline vertical={1pt}{0pt}{dashed}]{$E=mc^2$}
\end{document}

Easier version

tcolorbox provides nice features for boxes and frames etc. I've defined a \dashedbox command, that has a dashed frame of 1pt width and white background (colback=white), the usual frame is not drawn (boxrule=0pt). In order to provide equal heights, a equal height group is used.

All settings can be overruled by using the optional parameter of \dashedbox (as have been done for the second example!)

\documentclass{article}

\usepackage[most]{tcolorbox}

\newtcbox{\dashedbox}[1][]{equal height group=dashedbox,
  nobeforeafter,
  colback=white,
  boxrule=0pt,
  enhanced jigsaw,
  borderline horizontal={1pt}{0pt}{dashed},
  borderline vertical={1pt}{0pt}{dashed},
  #1
}

\begin{document}
\dashedbox{$E=mc^2$} \dashedbox[colback=yellow]{$E^2=(mc^2)^2 + (pc)^2$}
\end{document}

Next update

\documentclass{article}

\usepackage[most]{tcolorbox}

\newtcbox{\dashedbox}[1][]{
  math upper,
  baseline=0.4\baselineskip,
  equal height group=dashedbox,
  nobeforeafter,
  colback=white,
  boxrule=0pt,
  enhanced jigsaw,
  boxsep=0pt,
  top=2pt,
  bottom=2pt,
  left=2pt,
  right=2pt,
  borderline horizontal={0.5pt}{0pt}{dashed},
  borderline vertical={0.5pt}{0pt}{dashed},
  drop lifted shadow,
  #1
}

\begin{document}
Einstein said: $\dashedbox{E=mc^2} \; \dashedbox[colback=yellow]{E^2=(mc^2)^2 + (pc)^2}$
\end{document}