В течение недели я буду готовиться к экзамену.

Here в течение недели means during the week, over the course of a week, or for the span of a week.

In this sentence, it tells you the time period during which the action will happen:

• В течение недели = over the week / during the week
• я буду готовиться к экзамену = I will be preparing for the exam

So the whole sentence describes an ongoing activity happening over that time period.

This is a very common question.

In time expressions like this, Russian uses the fixed prepositional phrase в течение + Genitive, meaning during or in the course of.

So:

• в течение недели = during the week

By contrast, в течении is the prepositional case of the noun течение and is used in a more literal sense, such as talking about a current or flow:

• в течении реки = in the river’s current

So in your sentence, в течение is the correct form because it is a set expression meaning during.

Because в течение requires the genitive case.

The base form is:

• неделя = week

After в течение, it becomes:

• недели = of a week / week in the genitive singular

So:

• в течение недели = during the week

This is just a case pattern you need to memorize:

• в течение дня = during the day
• в течение месяца = during the month
• в течение года = during the year

Because готовиться is an imperfective verb, and the future of imperfective verbs is formed with:

• буду/будешь/будет... + infinitive

So:

• я буду готовиться = I will be preparing / I will prepare

This is called the compound future.

Russian does this regularly with imperfective verbs:

• я буду читать = I will be reading / I will read
• она будет работать = she will be working / she will work

The imperfective is used because the sentence focuses on the process of preparing, not on the completed result.

• буду готовиться = I will be preparing, I will spend time preparing

If you used a perfective verb such as подготовиться, the meaning would shift toward becoming fully prepared or finishing the preparation:

• Я подготовлюсь к экзамену = I will get prepared for the exam / I will finish preparing for the exam

So the difference is roughly:

• буду готовиться = focus on the ongoing activity
• подготовлюсь = focus on the completed outcome

Because готовиться is the standard Russian verb meaning to prepare oneself or to prepare for something.

Compare:

• готовить = to prepare something
• готовиться = to prepare oneself / to get ready / to prepare for

Examples:

• Я готовлю ужин. = I am preparing dinner.
• Я готовлюсь к экзамену. = I am preparing for the exam.

So the -ся matters a lot here. Without it, the verb would mean something different.

Because the verb готовиться takes the preposition к, and к requires the dative case.

So:

• экзамен = nominative
• к экзамену = to/for the exam, in the dative

This is the standard pattern:

• готовиться к уроку = to prepare for the lesson
• готовиться к поездке = to prepare for the trip
• готовиться к экзамену = to prepare for the exam

This is something you usually learn as part of the verb:

• готовиться к + dative

Экзамену is the dative singular form of экзамен.

The noun is masculine, so in the singular dative it often gets -у or -ю:

• экзамен → экзамену
• урок → уроку
• подарок → подарку

So in к экзамену, the ending -у shows that the noun is in the dative case after к.

Yes. Russian word order is flexible, and changing the order usually changes emphasis, not the core meaning.

Your sentence:

• В течение недели я буду готовиться к экзамену.

Another possible order:

• Я буду готовиться к экзамену в течение недели.

Both are natural. The difference is mostly stylistic:

• starting with В течение недели emphasizes the time frame
• starting with Я emphasizes the subject

Russian often puts important or topical information earlier in the sentence.

No. Russian has no articles, so there is no separate word for the or a/an.

That means:

• экзамен can mean an exam or the exam
• the exact meaning comes from context

In this sentence, к экзамену is naturally understood as for the exam, because the context makes it specific enough.