\documentclass[preview,border=12pt,varwidth]{standalone}
\usepackage{pgffor}
\usepackage{xparse}
\newcommand\XOR{\mathbin{\char`\^}}
\begin{document}
$\foreach \x in {1,...,3}{x\XOR\{}x\foreach \x in {1,...,3}{{\}}}$
\ExplSyntaxOn
\tl_set:Nn \g_tmpa_tl {}
\foreach \x in {1,...,3}
{
\tl_gput_right:Nn \g_tmpa_tl { x ^\bgroup }
}
\tl_gput_right:Nn \g_tmpa_tl { x }
\foreach \x in {1,...,3}
{
\tl_gput_right:Nn \g_tmpa_tl { \egroup }
}
$\tl_use:N \g_tmpa_tl $
\ExplSyntaxOff
\end{document}