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, S₁ and S₂ have same activity at time t = 0. At a later time, the activities of S₁ and S₂ are A₁ and A₂ , respectively. When S₁ and S₂ have just completed their 3^rd and 7^th half-lives, respectively, the ratio $\frac{{\mathrm{A}}_1}{{\mathrm{A}}_2}$ is ___________.