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1. $8^{2.4} \times 2^{3.7} \div {(16)}^{1.3} = 2^{?}$

A. 4.8

B. 5.7

C. 5.8

D. 7.1

Solution:

\begin{aligned} Let 8^{2.4} \times 2^{3.7} \div {(16)}^{1.3} = 2^{x} \\ Then, {(2^{3})}^{2.4} \times 2^{3.7} \div {(2^{4})}^{1.3} = 2^{x} \\ \Leftrightarrow 2^{(3 \times 2.4)} \times 2^{3.7} \div 2^{(4 \times 1.3)} = 2^{x} \\ \Leftrightarrow 2^{7.2} \times 2^{3.7} \div 2^{5.2} = 2^{x} \\ \Leftrightarrow 2^{x} = 2^{(7.2 + 3.7 - 5.2)} \\ \Leftrightarrow 2^{x} = 2^{5.7} \\ \Leftrightarrow x = 5.7 \end{aligned}

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