In a radioactive decay process, the activity is defined as $\mathrm{A}=-\frac{\mathrm{dN}}{\mathrm{dt}}$, where $N(t)$ is the number of radioactive nuclei at time $t$. Two radioactive sources, $S_1$ and $S_2$ have same activity at time $t=0$. At a later time, the activities of $S_1$ and $S_2$ are $A_1$ and $A_2$, respectively. When $S_1$ and $S_2$ have just completed their $3^{\text {rd }}$ and $7^{\text {th }}$ halflives, respectively, the ratio $A_1 / A_2$ is $\_\_\_\_$ .