Explanation:

- First, simplify the expression: \((0.16)^7 / (0.064)^3 \times (0.4)^2\).

- Convert decimals to fractions:

- \(0.16 = \left(\frac{16}{100}\right)^7\),

- \(0.064 = \left(\frac{64}{1000}\right)^3\),

- \(0.4 = \left(\frac{4}{10}\right)^2\).

- Simplify each fraction:

- \(\left(\frac{16}{100}\right)^7 = \left(\frac{4^2}{10^2}\right)^7 = \frac{4^{14}}{10^{14}}\),

- \(\left(\frac{64}{1000}\right)^3 = \left(\frac{4^3}{10^3}\right)^3 = \frac{4^9}{10^9}\),

- \(\left(\frac{4}{10}\right)^2 = \frac{4^2}{10^2}\).

- Substitute back:

- \(\frac{4^{14}}{10^{14}} / \frac{4^9}{10^9} \times \frac{4^2}{10^2} = \frac{4^{14 - 9 + 2}}{10^{14 - 9 + 2}} = \frac{4^7}{10^7}\).

- Determine the power of 0.4, since \(\frac{4^7}{10^7} = (0.4)^7\) as \(\frac{4^7}{10^7}\) simplifies to \((\frac{4}{10})^7\).

- Correct Answer: Option 3 - 7