Explanation:

- The problem presents a ratio pattern. The numbers 16 and 128 have a specific relationship.

- 128 is the cube of 16's square root: \( \sqrt{16} = 4 \), and \( 4^3 = 64 \).

- However, this doesn't directly solve the ratio in terms of powers.

- Instead, observe: \( 16 \times 8 = 128 \).

- To maintain this multiplication pattern: \( 4 \times 8 = 32 \).

- This leads to the conclusion that the consistent factor to multiply by in the pattern is 8.

- Given options, let's see if any match the answer derived from the pattern.

- Option 3: 8 is most consistent with the multiplication factor.

The correct answer seems to be Option 3: 8.