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1. $25^{2.7} \times 5^{4.2} \div 5^{5.4} = 25^{?}$

A. 1.6

B. 1.7

C. 3.2

D. 3.6

Solution:

\begin{aligned} Let 25^{2.7} \times 5^{4.2} \div 5^{5.4} = 25^{x} \\ Then, 25^{2.7} \times 5^{(4.2 - 5.4)} = 25^{x} \\ \Leftrightarrow 25^{2.7} \times 5^{(- 1.2)} = 25^{x} \\ \Leftrightarrow 25^{2.7} \times \frac{1}{5^{1.2}} = 25^{x} \\ \Leftrightarrow \frac{25^{2.7}}{{(5^{2})}^{0.6}} = 25^{x} \\ \Leftrightarrow \frac{{(25)}^{2.7}}{{(25)}^{0.6}} = 25^{x} \\ \Leftrightarrow 25^{x} = 25^{(2.7 - 0.6)} = 25^{2.1} \\ \Leftrightarrow x = 2.1 \end{aligned}

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