  In this short note we prove that every tournament contains the $k$-th power
of a directed path of linear length. This improves upon recent results of
Yuster and of Gir\~ao. We also give a complete solution for this problem when
$k=2$, showing that there is always a square of a directed path of length
$\lceil 2n/3 \rceil-1$, which is best possible.
