Powerless means lacking strength, ability, or authority. If nothing you do stops your dog from barking, you're powerless to make her be quiet.
A person who doesn't have the power they need to accomplish something can be described as powerless. A flustered substitute teacher is powerless to silence a chattering classroom, and citizens who don't vote are powerless to change their elected representatives in Congress. Power, "strength or vigor," can be traced back to a root meaning "power" or "lord." When you add the suffix -less, or "lacking," you get powerless.