Does the absolute value operator pick up dimension?

Question

My specific question is whether the quantity $\rho = k\times | xyz|$, has the dimension of $k$, or it has the dimension of $k\times xyz$?

Answer 1

$|xyz|\,$ is either $\,xyz\,$ or $\,-xyz\,$ depending on signs, so $\,|xyz|\,$ always has the same dimension as $\,xyz\,$.