[Tex/LaTex] How to properly subscript in a superscripted fraction

amsmathfractionssubscriptssuperscripts

the title says it all. It attached a MWE to display the different relative sizes of a subscript within a normal fraction and a superscripted fraction. As you can see, in the superscripted fraction the subscripted letters have the same size as the other letters. How can I change them to be smaller?

  \documentclass[a4paper]{article}
  \usepackage{amsmath}
  \begin{document}
    $e^\frac{E_{A}}{k_{B} T}$
    $\frac{E_{A}}{k_{B} T}$
  \end{document}

Best Answer

\displaystyle won't help you here, since your fraction is in the exponent.

a recommended approach when $e$ is involved is to use the operator name "exp":

$\exp\left(\frac{E_{A}}{k_{B} T}\right)$

\exp is already defined in plain tex and latex.