  For a fixed integer $r\ge1$, we say $k$-tuple integers $(x_1,\ldots,x_k)$ are
relatively $r$-prime if there exists no prime $p$ such that all $k$ integers is
multiple of $p^r$. Benkoski proved that the number of relatively $r$-prime
$k$-tuple integers in $[1,x]^k$ is $x^k/\zeta(rk)+$(Error term). We showed that
the exact order of error term is $x^{k-1}$ for $rk\ge3$ and $k\not=1$.
