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1. Simplify : $\frac{343 \times 49}{216 \times 16 \times 81} = ?$

A. $\frac{7^{5}}{6^{7}}$

B. $\frac{7^{5}}{6^{8}}$

C. $\frac{7^{6}}{6^{7}}$

D. $\frac{7^{4}}{6^{8}}$

Solution:

\begin{aligned} \frac{343 \times 49}{216 \times 16 \times 81} \\ = \frac{7^{3} \times 7^{2}}{6^{3} \times 2^{4} \times 3^{4}} \\ = \frac{7^{(3 + 2)}}{6^{3} \times {(2 \times 3)}^{4}} \\ = \frac{7^{5}}{6^{3} \times 6^{4}} \\ = \frac{7^{5}}{6^{(3 + 4)}} \\ = \frac{7^{5}}{6^{7}} \end{aligned}

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