documentclass{article}
usepackage{xfrac}

begin{document}
Works in text mode sfrac{1}{2} and in math mode $sfrac{1}{2}$.

In exponents: $e^{sfrac{1}{2}}$
end{document}

documentclass{article}
usepackage{xfrac}    % for xfrac macro
usepackage{nicefrac} % for nicefrac macro
usepackage{amsmath}  % for dfrac macro
newcommand{e}{mathrm{e}}
begin{document}
some words $e^{frac{1}{2x}}$ $e^{dfrac{1}{2x}}$ $e^{1/2x}$ $e^{nicefrac{1}{2x}}$ $exp(sfrac{1}{2x})$ some more words
end{document}

documentclass{article}
usepackage[nice]{nicefrac}
begin{document}
  $e^{1/2}$ $e^{(1/2)}$ $e^{0.5}$

  With verb|nicefrac|

    $e^{nicefrac{1}{2}}$

end{document}

documentclass{article}
usepackage[ugly]{nicefrac}
begin{document}
  With verb|nicefrac|

    $e^{nicefrac{1}{2}}$

end{document}