Learn Hardcore Ukrainian: Я повинен відповісти на питання вчителя.

Повинен is a short-form adjective used as a modal “must/have to.” It agrees in gender and number with the subject. Since Я here is implicitly masculine, we use повинен. If the speaker were female, it would be повинна.

Why is відповісти in the infinitive, not a conjugated form?

After a modal like повинен, the main verb remains in the infinitive to express the action you must perform. Hence відповісти (to answer) rather than відповідаю, відповість etc.

Why do we need the preposition на before питання?

The verb відповісти governmentally takes на + accusative to indicate the target of the answer. So you always say відповісти на щось (“answer something”).

What case is питання, and why does it look identical to the nominative?

Here питання is in the accusative case (the object of відповісти). For neuter, inanimate nouns of the second declension, the accusative form is identical to the nominative.

What case is вчителя, and what does it express?

Вчителя is the singular genitive of вчитель (teacher). It expresses possession/relationship: literally “the question of (the) teacher.”

Can I omit Я and still be correct?

Yes. Ukrainian allows dropping subject pronouns when the verb or context makes the subject clear. You could say Повинен відповісти на питання вчителя, though including Я adds emphasis on the speaker.

Is there a more colloquial way to say “I have to answer the teacher’s question”?

Yes. You can use:
• Я мушу відповісти на питання вчителя. (мусити = colloquial “must”)
• Мені треба відповісти на питання вчителя. (треба is impersonal and takes a dative: мені)