Discussion
If \((1.001)^{1259} = 3.52\) and \((1.001)^{2062} = 7.85\), then \((1.001)^{3321} =\)
Answer: D
The value is about 27.64.
The exponents add: \(1259 + 2062 = 3321\). So by the law of indices
\[ \begin{aligned} (1.001)^{3321} &= (1.001)^{1259}\times(1.001)^{2062} \\ &= 3.52 \times 7.85 = 27.632 \end{aligned} \]
which rounds to the option 27.64. 11.37 adds the two values instead of multiplying them, 4.33 is their difference, and 2.23 is their ratio; none follows from the rule \(a^{m}a^{n} = a^{m+n}\).
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