  For $x\geq 3$, we define $w(x)$ as the highest integer $w$ for which there
exist integers $m, y\geq 1$ and $1\leq n_1<\dots<n_m\leq x$ such that
$n_1\cdots n_m=y^w$. We show that \[w(x)=x\exp\big(-(\sqrt{2}+o(1))\sqrt{\log
x\log\log x}\big).\]
