Practice Test Discussion

$\frac{343 \times 49}{216 \times 16 \times 81} = ?$

[Bank of Baroda (PO), 2010]

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

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

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

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

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

Explanation

$\begin{array}{l} Here, \\ \Rightarrow \frac{7^{3} \times 7^{2}}{6^{3} \times 4^{2} \times 9^{2}} \\ [\begin{array}{l} ∵ 343 = 7^{3}, 49 = 7^{2} \\ 216 = 6^{3}, 16 = 4^{2}, 81 = 9^{2} \end{array}] \\ \Rightarrow \frac{7^{5}}{6^{3} \times {(4 \times 9)}^{2}} = \frac{7^{5}}{6^{3} \times {(6)}^{4}} \\ = \frac{7^{5}}{6^{3} \times 6^{4}} = \frac{7^{5}}{6^{7}} \end{array}$

Hence Option A is correct.

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