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1. ${(6)}^{4} \div {(36)}^{3} \times 216 = 6^{(? - 5)}$

A. 1

B. 4

C. 6

D. 7

Solution:

\begin{aligned} Let , \\ {(6)}^{4} \div {(36)}^{3} \times 216 = 6^{(x - 5)} \\ Then, \\ 6^{(x - 5)} = {(6)}^{4} \div {(6^{2})}^{3} \times 6^{3} \\ \Rightarrow 6^{(x - 5)} = 6^{4} \div 6^{(2 \times 3)} \times 6^{3} \\ \Rightarrow 6^{(x - 5)} = 6^{4} \div 6^{6} \times 6^{3} \\ \Rightarrow 6^{(x - 5)} = 6^{(4 - 6 + 3)} \\ \Rightarrow 6^{(x - 5)} = 6 \\ \Rightarrow x - 5 = 1 \\ \Rightarrow x = 6 \end{aligned}

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