If you convince your administrator to enable mhchem here – chemistry.SE does have it – then you could make use of MathJax/mhchem's \pu
command.
$1.38 \times 10^{-23} \, \mathrm{J\,K^{-1}}$
could then be written as
\pu{1.38E-23 J K^-1}
See how it renders at chemistry.SE.
Background information:
MathJax is a LaTeX implementation, written in JavaScript. It is not a complete TeX engine, it just does a very similar job when looked at fromt he outside. Because it is completely different at the inside, one cannot simply load LaTeX packages. Instead, one has to create a completely new package in JavaScript. That's the reason, one cannot simply load siunitx with MathJax. You would need somebody to rewrite the whole behavior for a completely different framework. With mhchem, I did such an reimplementation. Because TeX and JavaScript are so different, the two packages look very different inside. They even behave slightly differently (with MathJax/mhchem having more features than the original LaTeX/mhchem).