A reaction has the rate law rate = k[A]^(1/2)[B]²…

The rate law is $\text{rate} = k[\text{A}]^x[\text{B}]^y$, and the orders come from experiment. When only $[\text{A}]$ changes by a factor $f$, the rate changes by $f^x$. For overall order $n$, the unit of $k$ is $\text{L}^{n-1}\ \text{mol}^{1-n}\ \text{s}^{-1}$.