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1. Simplify : $\frac{16 \times 32}{9 \times 27 \times 81} = ?$

A. ${(\frac{2}{3})}^{9}$

B. ${(\frac{2}{3})}^{11}$

C. ${(\frac{2}{3})}^{12}$

D. ${(\frac{2}{3})}^{13}$

Solution:

\begin{aligned} \frac{16 \times 32}{9 \times 27 \times 81} \\ = \frac{2^{4} \times 2^{5}}{3^{2} \times 3^{3} \times 3^{4}} \\ = \frac{2^{(4 + 5)}}{3^{(2 + 3 + 4)}} \\ = \frac{2^{9}}{3^{9}} \\ = {(\frac{2}{3})}^{9} \end{aligned}

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