The units of rate constant for the reaction obeying rate expression, $\mathrm{r}=\mathrm{k}\left[\mathrm{A}\right][\mathrm{B}{]}^{2/3}$ is 

units for rate constant are: L^(n–1) mol^(1–n) s^–1.

Given, $\mathrm{r}=\mathrm{k}\left[\mathrm{A}\right][\mathrm{B}{]}^{2/3}$

n=1+2/3=5/3

$\therefore$The units of rate constant are, 

L^(2/3) mol^-(2/3)time^-1.