This is the 5166th most frequent Korean word.
놓게
"놓게" is a form of the verb "놓다," meaning "let (someone) put/place" or "allow to release."
In this sentence, '놓게' is part of the verb phrase '열어 놓게 되다', where '놓다' combined with '되다' indicates an action completed with the state that arises afterwards. It expresses a situation that resulted from the speaker's actions.
문을 강아지가 나가도록 열어 놓게 되었어요.
I ended up leaving the door open for the dog to go out.
Here, '놓게' is used as part of '해 놓게 하다', which suggests the completion of preparation through an indirect action influencing someone to do so. It shows the causative nature of the speaker's intention.
학교에 일찍 가게 하려면 준비를 빨리 해 놓게 해줘야 해요.
To make someone go to school early, you need to help them prepare quickly ahead of time.
In this case, '놓게' appears in '눌러 놓게 하다', implying the action of pressing the button completed to enable the machine's functioning. It stresses the necessity of the preliminary action for the desired state to occur.