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1. (0.04)² ÷ (0.008) × (0.2)⁶ = (0.2)^?

A. 5

B. 6

C. 8

D. 9

Solution:

\begin{aligned} Let {(0.04)}^{2} \div (0.008) \times {(0.2)}^{6} = {(0.2)}^{x} \\ Then, {(0.2)}^{x} = {[{(0.2)}^{2}]}^{2} \div {(0.2)}^{3} \times {(0.2)}^{6} \\ \Leftrightarrow {(0.2)}^{x} = {(0.2)}^{(2 \times 2)} \div {(0.2)}^{3} \times {(0.2)}^{6} \\ \Leftrightarrow {(0.2)}^{x} = {(0.2)}^{4} \div {(0.2)}^{3} \times {(0.2)}^{6} \\ \Leftrightarrow {(0.2)}^{x} = {(0.2)}^{(4 - 3 + 6)} \\ \Leftrightarrow {(0.2)}^{x} = {(0.2)}^{7} \\ \Leftrightarrow x = 7 \end{aligned}

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