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1. (1000)¹² ÷ (10)³⁰ = ?

A. (1000)²

B. 10

C. 100

D. (100)¹²

Solution:

\begin{aligned} \frac{{(1000)}^{12}}{{(10)}^{30}} \\ = \frac{{(10^{3})}^{12}}{{(10)}^{30}} \\ = \frac{{(10)}^{(3 \times 12)}}{{(10)}^{30}} \\ = \frac{{(10)}^{36}}{{(10)}^{30}} \\ = {(10)}^{(36 - 30)} \\ = 10^{6} \\ = {(10^{3})}^{2} \\ = {(1000)}^{2} \end{aligned}

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