Learn Hardcore Russian: Я прошу учителя повторить правило.

Dictionary form (nominative): учитель (teacher)
Genitive singular: учителя
Accusative singular (for animate masculine nouns): same form as genitive → учителя

In this sentence, учителя is the direct object of прошу (I ask), so it must be in the accusative. Because the noun is animate and masculine, the accusative takes the same ending as the genitive, not the nominative.

That is why you see учителя, not учитель.

Could I say Я прошу учитель instead of Я прошу учителя?

No, Я прошу учитель is incorrect.

You need the accusative form for the direct object of прошу:

Я прошу кого? – учителя (whom do I ask? the teacher)

Using the nominative учитель would sound like you are starting a new clause where учитель is the subject (as if you were going to say The teacher does something), but nothing follows, so it is ungrammatical in this context.

Who is actually repeating the rule here — me or the teacher?

The one who is supposed to repeat the rule is the teacher, not я.

The pattern is:

просить кого-то сделать что-то – to ask someone to do something

So:

Я прошу учителя (I ask the teacher)
повторить правило (to repeat the rule)

By default, in Russian, with this pattern, the person in the accusative (учителя) is the one who will perform the action of the infinitive (повторить).

If you want to make it extra explicit, you can say:

Я прошу учителя, чтобы он повторил правило.
(I ask the teacher so that he would repeat the rule.)

Why is повторить in the infinitive, and not a finite form like повторяет or повторит?

Verbs of asking, telling, ordering, etc., often take an infinitive in Russian to indicate what action you want someone to do:

просить кого-то сделать что-то – to ask someone to do something
говорить кому-то сделать что-то – to tell someone to do something
советовать кому-то сделать что-то – to advise someone to do something

So you say:

Я прошу учителя повторить правило.
literally: I ask the teacher to repeat the rule.

If you used повторяет or повторит, it would describe what someone is doing / will do, not what you want them to do, and you would need a different structure, e.g.:

Я прошу, и учитель повторяет правило. – I ask, and the teacher repeats the rule. (two separate actions)

Why is the perfective повторить used, and not the imperfective повторять?

The choice of повторить (perfective) here emphasizes a single, complete action:

повторить – to repeat once / to repeat fully (complete event)
повторять – to be repeating, to repeat regularly, to be in the process of repeating

In this context, you are asking the teacher to repeat the rule once (for you now), which is naturally expressed with the perfective:

Я прошу учителя повторить правило. – I ask the teacher to (once) repeat the rule.

Using повторять would sound odd here; it would suggest asking for an ongoing or habitual process, which is not what is usually meant.

What case is правило, and why does it look the same as its dictionary form?

Правило is neuter singular, and in Russian:

Neuter inanimate nouns have the same form for nominative and accusative:
- Nominative: правило
- Accusative: правило

In this sentence, правило is the direct object of повторить:

повторить что? – правило

Grammatically it is accusative, but its form coincides with the nominative, so you do not see a visible change.

Can I change the word order, for example: Учителя я прошу повторить правило or Я прошу повторить правило учителя?

1. Учителя я прошу повторить правило.
This is grammatically correct. It just changes the emphasis:

Учителя я прошу повторить правило.
Focuses on учителя (It is the teacher that I am asking to repeat the rule.)

Russian allows fairly flexible word order for nuance and emphasis, as long as the cases are correct.

2. Я прошу повторить правило учителя.
Also grammatically possible, but now учителя is naturally read as genitive:

правило учителя – the teacher’s rule

So this tends to be understood as:

I ask (someone) to repeat the teacher’s rule.

It no longer clearly means I ask the teacher to repeat the rule; the role of учителя has changed. So for the original meaning, you should keep:

Я прошу учителя повторить правило.

What is the difference between просить and спрашивать / спросить, since they all translate as “ask”?

Russian makes a clear distinction:

просить – to ask for something / someone to do something
- Я прошу учителя повторить правило. – I ask the teacher to repeat the rule.
- Я прошу воду. – I ask for water.
спрашивать / спросить – to ask a question, to inquire
- Я спрашиваю учителя. – I am asking the teacher (a question).
- Я спрашиваю учителя, что это значит. – I ask the teacher what this means.

In your sentence, you are requesting an action (repeat), so просить is the correct choice.

What is the difference between прошу and попрошу? Which should I use here?

Both come from the verb просить / попросить:

прошу – present tense, imperfective
- ongoing / general asking: I ask / I am asking
- Я прошу учителя повторить правило.
попрошу – future tense, perfective
- a single completed act of asking in the future: I will ask
- Я попрошу учителя повторить правило. – I will ask the teacher to repeat the rule.

In your sentence, if you are currently asking, you should use прошу.
Use попрошу when talking about what you will do later.

Can I say Я прошу учителя, чтобы он повторил правило instead? Is there a difference in meaning?

Yes, you can. The meaning is essentially the same, but the structure is different:

Я прошу учителя повторить правило.
Verb of asking + infinitive.
Я прошу учителя, чтобы он повторил правило.
Verb of asking + subordinate clause with чтобы.

Nuance:

The infinitive version is more compact and very natural in speech.
The чтобы-clause is slightly more explicit (you clearly say он is the one doing it) and can feel a bit more formal or careful in some contexts.

Both are correct and common; in everyday speech, the infinitive version is extremely frequent.

How do you stress and pronounce each word in Я прошу учителя повторить правило?

Stresses (capital letters show the stressed syllable):

Я – [ya]
прошу́ – pra-SHÚ
учи́теля – u-CHÍ-tye-lya
повторить́ – paf-ta-RÍTʹ
пра́вило – PRÁ-vi-la

Approximate IPA:

Я – [ja]
прошу́ – [prɐˈʂu]
учи́теля – [ʊˈt͡ɕitʲɪlʲə]
повторить́ – [pəftɐˈrʲitʲ]
пра́вило – [ˈpravʲɪlə]

Natural connected speech will link sounds a bit, but the stress positions stay the same.

Is Я прошу учителя повторить правило polite enough to say to a real teacher?

Grammatically it is fine, but in real-life interaction you usually soften it a bit. For example:

Учитель, повторите, пожалуйста, правило.
(Teacher, please repeat the rule.)

or more formal:

Извините, пожалуйста, повторите, пожалуйста, правило.
(Excuse me, please repeat the rule.)

Your sentence can sound a bit like you’re describing the situation to someone else (narration) rather than directly addressing the teacher. For direct speech, using вы-form (повторите) and пожалуйста is more natural and polite.