(0.04)² ÷ (0.008) × (0.2)⁶ = (0.2)^?

15
26
38
4None of these

Answer:- 1

Explanation:-

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}

$\eqalign{ & {\text{Let }}{\left( {0.04} \right)^2} \div \left( {0.008} \right) \times {\left( {0.2} \right)^6} = {\left( {0.2} \right)^x} \cr & {\text{Then,}}{\left( {0.2} \right)^x} = {\left[ {{{\left( {0.2} \right)}^2}} \right]^2} \div {\left( {0.2} \right)^3} \times {\left( {0.2} \right)^6} \cr & \Leftrightarrow {\left( {0.2} \right)^x} = {\left( {0.2} \right)^{\left( {2 \times 2} \right)}} \div {\left( {0.2} \right)^3} \times {\left( {0.2} \right)^6} \cr & \Leftrightarrow {\left( {0.2} \right)^x} = {\left( {0.2} \right)^4} \div {\left( {0.2} \right)^3} \times {\left( {0.2} \right)^6} \cr & \Leftrightarrow {\left( {0.2} \right)^x} = {\left( {0.2} \right)^{\left( {4 - 3 + 6} \right)}} \cr & \Leftrightarrow {\left( {0.2} \right)^x} = {\left( {0.2} \right)^7} \cr & \Leftrightarrow x = 7 \cr}$