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

Let us consider the problem:
Let the order $=1+\frac{2}{3}=\frac{5}{3}$
Hence,
Units of rate constant = mole 

$={\text{mole}}^{1-\frac{5}{3}}{\text{lit}}^{\frac{5}{3}-1}{\text{time}}^{-1}={\text{mole}}^{-2/3}{\text{litre}}^{2/3}{\text{time}}^{-1}$