sensei no hatuon wo rokuonsite oku to, ie de nando mo kikete benri da.

〜ておく usually means do something in advance or do something and leave it that way for later use.

So 録音しておく is not just record. It has the nuance of:

• record it ahead of time
• record it so you can use it later

In this sentence, that later use is explained in the next part: you can listen to it many times at home.

Here, と is the conditional particle meaning if / when.

So:

• 先生の発音を録音しておくと
  = If you record the teacher’s pronunciation / When you record the teacher’s pronunciation

This と often describes a natural result or consequence. The idea is:

• If you do that, then naturally it becomes convenient because you can listen later.

So the full flow is:

• 録音しておくと → if you record it in advance
• 家で何度も聞けて便利だ → it’s convenient because you can listen to it many times at home

聞けて comes from the potential form 聞ける, which means can listen or can hear.

• 聞く = to listen
• 聞ける = can listen
• 聞けて = te-form of 聞ける

So:

• 家で何度も聞けて便利だ = It’s convenient because you can listen to it many times at home

If it were 聞いて, it would mean listening, not being able to listen. The sentence specifically wants the idea of ability/opportunity.

The て-form can connect ideas in a loose way, and one common nuance is because / and so.

So:

• 聞けて便利だ literally feels like
  you can listen to it, and it’s convenient

In natural English, that becomes:

• it’s convenient because you can listen to it
• it’s convenient since you’re able to listen to it

This is a very common Japanese way of linking a reason to an evaluation.

Literally, it means the teacher’s pronunciation.

Here の connects two nouns:

• 先生 = teacher
• 発音 = pronunciation

So this is the pronunciation used by the teacher, or the teacher’s model pronunciation.

In context, it usually means something like:

• the way the teacher pronounces words
• the teacher’s spoken model
• the teacher’s pronunciation for study purposes

It does not mean pronunciation about the teacher. It means pronunciation that belongs to or is produced by the teacher.

を marks the direct object of the verb.

The verb here is 録音する = to record.

So:

• 先生の発音を録音する = to record the teacher’s pronunciation

The thing being recorded is 先生の発音, so it takes を.

Because で marks the place where an action happens.

Here, the action is 聞ける / listen.

So:

• 家で聞く = listen at home

By contrast, に is usually used for:

• destination: 家に帰る = go home
• existence: 家にいる = be at home

Since listening is an action happening in that place, で is the correct particle.

何度も means:

• many times
• again and again
• repeatedly

It is made from:

• 何度 = how many times
• も = adds the sense of as many as / even / emphasis

So 何度も聞けて means:

• can listen to it many times
• can listen to it over and over

The も helps give that repeated, emphatic feeling.

Japanese often leaves out subjects when they are obvious from context.

This sentence is making a general statement or giving practical advice, so the understood subject is something like:

• you
• one
• it is useful to

So the sentence naturally means something like:

• If you record the teacher’s pronunciation, it’s convenient because you can listen to it many times at home.

Japanese does this very often, especially when the listener can easily infer the subject.

便利 means convenient.

It behaves like a na-adjective, so in plain form:

• 便利だ = is convenient

This sentence is in plain style, which is why it ends with だ.

A polite version would be:

• 先生の発音を録音しておくと、家で何度も聞けて便利です。

So the final 便利だ is simply the speaker’s evaluation of the whole situation: it is convenient.

Yes. The difference is mainly nuance.

• 録音する = to record
• 録音しておく = to record in advance / to record and keep for later

So しておく adds the idea of preparation and future usefulness.

In this sentence, that nuance matters a lot, because the point is not merely the act of recording. The point is:

• record it now
• so that later, at home, you can listen to it many times

That is exactly the kind of situation where 〜ておく is commonly used.