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1. The value of $(\frac{9^{2} \times 18^{4}}{3^{16}})$ is = ?

A. $\frac{3}{2}$

B. $\frac{4}{9}$

C. $\frac{16}{81}$

D. $\frac{32}{243}$

Solution:

\begin{aligned} (\frac{9^{2} \times 18^{4}}{3^{16}}) \\ = \frac{9^{2} \times {(9 \times 2)}^{4}}{3^{16}} \\ = \frac{{(3^{2})}^{2} \times {(3^{2})}^{4} \times 2^{4}}{3^{16}} \\ = \frac{3^{4} \times 3^{8} \times 2^{4}}{3^{16}} \\ = \frac{3^{(4 + 8)} \times 2^{4}}{3^{16}} \\ = \frac{3^{12} \times 2^{4}}{3^{16}} \\ = \frac{2^{4}}{3^{(16 - 12)}} \\ = \frac{2^{4}}{3^{4}} \\ = \frac{16}{81} \end{aligned}

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