undonghago naseo baega gopayo.

-고 나서 means after doing... or once ... is finished.

So 운동하고 나서 means after exercising.

It connects two actions or states in sequence:

• 운동하고 나서 = after exercising
• 배가 고파요 = I’m hungry / my stomach is hungry

Compared with just -고, -고 나서 more clearly emphasizes that the first action happens first and is completed before the second part.

Here, 운동하다 is a very common verb meaning to exercise.

Because 운동하다 is treated as a single verb, you often just conjugate 하다:

• dictionary form: 운동하다
• connective form: 운동하고

You can sometimes see 운동을 하다, especially when treating 운동 more like a noun, but 운동하다 is extremely natural and common.

So:

• 운동하고 나서 = perfectly natural
• 운동을 하고 나서 = also possible, but a little less compact

In Korean, 고프다 works like an adjective meaning to be hungry, and the thing that is hungry is marked with the subject particle 이/가.

So:

• 배 = stomach
• 배가 고파요 = the stomach is hungry → I’m hungry

This is the normal Korean way to express hunger.

If you used 배는, that would add contrast or topic emphasis:

• 배는 고파요 = As for my stomach, it’s hungry / I am hungry though...

But the basic neutral form is 배가 고파요.

That is just the natural Korean expression.

Korean often expresses physical states through body-related words:

• 배가 고파요 = I’m hungry
• 목이 말라요 = I’m thirsty
• 머리가 아파요 = My head hurts / I have a headache

So even though the literal structure involves stomach, the real meaning is simply I’m hungry.

This comes from how 고프다 changes when you add -아요/어요.

The stem is 고프-. With this type of adjective, the ㅡ drops before -아/어요:

• 고프다
• 고프 + 아요
• 고파요

So 고파요 is the correct natural form.

This same pattern happens with other ㅡ-ending words too.

고파요 is in the polite informal style, often called the -요 form.

It is appropriate for:

• everyday conversation
• speaking politely to strangers
• speaking to teachers, coworkers, or people you do not know very well

Other levels:

• casual: 배고파
• formal: 배가 고픕니다

So 배가 고파요 is a very standard, useful form for daily speech.

Yes. 배고파요 is very common in everyday speech.

Both are natural:

• 배가 고파요
• 배고파요

The version with 배가 shows the structure more clearly, which is why learners often see it in textbooks. In real conversation, people very often say 배고파요.

Yes. That also means I’m hungry after exercising.

Comparison:

• 운동하고 나서 배가 고파요 = very natural in conversation; emphasizes doing exercise and then being hungry
• 운동한 후에 배가 고파요 = also correct; slightly more formal or written-sounding in some situations

Both are good, but -고 나서 is especially common in spoken Korean.

Because -고 나서 already shows the sequence: first the exercise happens, then the hunger.

The main sentence 배가 고파요 is in the present because it describes the current state:

• I’m hungry now, after exercising

Korean does not need to put the first verb in a separate past form here. The idea of after doing it is already built into -고 나서.

If the whole situation were in the past, then the main predicate would usually change:

• 운동하고 나서 배가 고팠어요 = I was hungry after exercising

You could, but it is less clear and less natural if you specifically want to mean after exercising.

• 운동하고 나서 배가 고파요 clearly means after exercising, I’m hungry
• 운동하고 배가 고파요 can sound more like I exercise and I’m hungry or just a looser connection between the two ideas

So if your goal is to show clear time order, -고 나서 is the better choice.