In a radioactive decay process, the activity is defined as A=-\frac{d N}{d t}, 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 }} half-lives, respectively, the ratio \frac{A_1}{A_2} is _____________