[Tex/LaTex] Summation as exponent

Question

 x^{\displaystyle\sum_{k=1}^n {n \choose k}p^k + 1}

How can I make the exponent look smaller?

Answer 1

Instead fo trying to accommodate such a big expression as a superscript, I'd suggest you to use a name for it and then explain this name:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\[
x^{\alpha},\quad\text{where } \alpha=\sum_{k=1}^n \binom{n}{k} p^k + 1.
\]

$x^{\alpha},\text{ where } \alpha=\sum_{k=1}^n \binom{n}{k} p^k + 1$.

\end{document}

Also, \choose is an old command; use \binom{}{} instead.