  In this note we show that every tournament on $n$ vertices contains the
$k$-th power of a directed path of length $n/2^{6k+7}$, which improves upon the
recent bound of Scott and Kor\'{a}ndi of $n/2^{2^{3k}}$. By doing so, we get an
inverse exponential dependence on $k$, which is best possible as Yuster
recently showed an upper bound of $kn/{2^{k/2}}$.
