-어 놓다

V + 아/어 놓다 This indicates the continued state after an action has been completed with a specific intention. (I’ve left~)

에어컨을 켜 놓았다.

I've left the air conditioner turned on.

언니가 밥을 해 놓고 출근했다.

My sister left the rice cooked and went to work.

집 청소 먼저 해 놓으세요.

Please clean the house first.

• It can be replaced with -어 두다. However, while -어 놓다 simply states that an action is left as it is(whether intended or not), -어 두다 adds the nuance of doing something in advance for later use or someone’s benefit.
• 에어컨을 켜 놓았다 (O): just states the AC was left on.

에어컨을 켜 두었다 (O): left it on in preparation for later.

• 창문을 깨 놓았다 (O): just states the window was broken.

창문을 깨 두었다 (?): unnatural, since it’s hard to imagine breaking a window for later use or for someone else’s benefit.