This is the 519th most frequent Korean word.
하기
"하기" in Korean means "doing" or "the act of doing."
'하기' is utilized here to nominalize the verb '운동하다' (to exercise), allowing it to function as the subject of the sentence.
운동하기는 건강에 좋아요.
Exercising is good for your health.
'하기' nominalizes the verb '하다' (to do), specifying the general act of doing as the object of the phrase '시작했어요' (started).
요리를 배우기 전에 준비 작업을 하기 시작했어요.
Before learning to cook, I started the preliminary preparations.
'하기' is used as a verbal noun to indicate the act of studying (공부하기), enabling its integration with '위해' (for the purpose of).