If both $\mathrm{dc}/\mathrm{dt} \&$specific rate have same units, then rate law is

$$\begin{gathered} \frac{\mathrm{dc}}{\mathrm{dt}}=\mathrm{rate} \\ \mathrm{K}=\mathrm{specific} \mathrm{rate} \end{gathered}$$

Both are having same units

Rate law is $\frac{\mathrm{dc}}{\mathrm{dt}}\left(\mathrm{rate}\right) =\mathrm{K} {\left[\mathrm{R}\right]}^{\mathrm{n}}$

Concentration of reactants =[R]

n = order of the reaction

Given units of rate and units of rate constant are same, this is possible only when  [R]¹ = 1;

Rate = K this possible only when n = 0 i.e for zero order reactions.