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In a radioactive decay process, the activity is defined as A = dN/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 3rd and 7th half-lives, respectively, the ratio \(\frac{A_1}{A_2}\) is ________.

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From (i) and (ii),

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