Which statement is true regarding a 75-meter power-driven vessel underway at night?

A 75-meter power-driven vessel underway at night is required to exhibit specific navigation lights to ensure safe operation and visibility to other vessels. The correct answer states that she must exhibit forward and after masthead lights. This requirement complies with the International Regulations for Preventing Collisions at Sea (Colreg), which dictate the lighting configurations for different vessel sizes and types.

For a power-driven vessel of this length, it is critical to have outward-facing lights that are visible from different angles to indicate the vessel's position, direction, and status. The forward masthead light typically shines forward and slightly to the sides, while the after masthead light shines aft, ensuring that vessels approaching from any direction can identify the power-driven vessel accurately.

The other options suggest limited or incorrect lighting configurations that would not meet the standards set by maritime regulations, potentially leading to confusion or collisions with other vessels in the vicinity. Thus, it is essential for vessels, especially those over 50 meters like the 75-meter one in this scenario, to display the appropriate lights as outlined in the regulations to promote safety on the water.