How do I solve this problem:
You buy a 75W lightbulb in Europe where electricity is delivered to homes at 240V. If you use the lightbulb back in the USA at 120 V, what will it's power output be?
They probably want you to assume constant resistance, with P = V^2/R
Half the voltage would then produce one-fourth the power, if by "power " you mean both light and heat power.
In actual fact, the resistance will be much less at the lower voltage (and filament temperature) because that is the way tungsten behaves.
It the bulb is a compact fluorescent, the bulb may not "light" at all at the lower voltage.
Light bulbs are highly non-ideal resistors. They do not obey ohm's law.
Another problem is they do not define "output power". If they are referring to visible light only, that drops more rapidly that the consumed power input, because the filament becomes "red hot" instead of "white hot" as its temperature drops.
This is a poorly assigned question.