\documentclass[10pt]{article}
\usepackage[usenames]{color} % Farbunterstützung
\usepackage{amssymb}    % Mathe
\usepackage{amsmath} % Mathe
\usepackage[utf8]{inputenc} % Direkte Eingabe von Umlauten und anderen Diakritika
\usepackage{braket}

(-1)^p=(-1)^\{$P^{\prime}$\+$P^{\prime\prime}$\}
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  • 4
    Welcome! You cannot have (-1)^p=(-1)^ outside math mode. Try \documentclass{article} \begin{document} $(-1)^p=(-1)^{P^{\prime}+P^{\prime\prime}}$ or $(-1)^p=(-1)^{\{P^{\prime}+P^{\prime\prime}\}}$ \end{document}. – marmot Dec 6 at 17:16
  • 4
    You're also missing both a \begin{document} and an \end{document} directive. – Mico Dec 6 at 17:17

I believe this is what you're looking for. (I would also argue that writing ' is easier than ^{\prime} -- and that writing '' is a lot easier than ^{\prime\prime}.)

enter image description here

\documentclass{article}
\begin{document}
$(-1)^p=(-1)^{(P'+P'')}$
\end{document}

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