Breakdown of Я прошу вас подождать.
вы
you (plural or formal)
подождать
to wait
просить
to ask for, to request
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Questions & Answers about Я прошу вас подождать.
Why is подождать in the perfective aspect here?
Affirmative requests to do a specific, one-time action use the perfective aspect. Just like giving a direct affirmative command uses the perfective, asking someone to do it once uses the perfective infinitive подождать. If you were asking them not to wait, you would switch to the imperfective: я прошу вас не ждать.
How does this sentence connect to the lesson about imperative commands?
This sentence is a polite request rather than a direct command, so it uses an infinitive instead of an imperative. However, the aspect rules are very similar! If you turned this into a direct affirmative command, you would use the perfective imperative подождите. If you gave a negative command (do not wait), you would use the imperfective не ждите.
Why do we use прошу instead of спрашиваю for asking?
Russian uses two completely different verbs for asking. You use спрашивать when you want to ask a question to get information. You use просить (which conjugates to прошу for the I form) when you want to ask a favor or request that someone do something, as in this sentence.
What case is вас in this sentence?
It is in the accusative case. The verb просить (to request) takes a direct object, meaning the person you are asking is the direct target of the action. Вас is the accusative form of the formal or plural you, which is вы.