[Tex/LaTex] Displaystyle numbers in exponent

Question

In a math equation, I have

$$ e^{\dfrac{A+B}{B}} $$

which is simplified as

$$ e^{\dfrac{A}{B} + 1} $$

however the "1" is now too small and the equation aspect is not so nice.
Is there a way to have a "1" with the same dimensions of "A" and "B" without go back to the "small" \frac?

Answer 1

Don't you think one of these would look nicer?

 \documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{lmodern}
\usepackage{slantsc}
\newcommand\textscsl[1]{\textsc{\slshape#1}}

\begin{document}

   \[ e^{ \scriptscriptstyle\frac{A}{B}+ 1} \quad e^{\tfrac{\textscsl{a}}{\raisebox{0.3ex}{\textscsl{\scriptsize b}}} + 1} \quad e^{\tfrac{A}{B} + 1}\]%

\end{document}