Мне удалось попасть на выставку бесплатно.

Because удаться / удалось uses a different construction from English.

In this sentence, мне is in the dative case and marks the person to whom the success happened:

• мне удалось = I managed / I succeeded
• literally, something like to me, it succeeded

This verb is often used in an impersonal way, so Russian does not use я as the grammatical subject here.

Compare:

• Я смог попасть на выставку = I was able to get to the exhibition
• Мне удалось попасть на выставку = I managed to get to the exhibition, often with a sense that it was not easy, or that it worked out successfully

So мне удалось is a very natural pattern, even though it feels unusual from an English point of view.

Удалось is the past tense of удаться.

In this sentence, it means something like:

• managed to
• succeeded in
• was able to, and it worked out

It often suggests that there was some difficulty, uncertainty, or a successful outcome after effort.

So Мне удалось попасть на выставку бесплатно is not just a plain statement of ability. It suggests:

• I succeeded in doing it
• it worked out
• perhaps it was not guaranteed

That is why удалось can sound slightly stronger or more satisfying than a simple смог.

Because this is an impersonal past-tense construction.

In Russian past tense, verbs normally agree with a subject:

• он смог
• она смогла
• они смогли

But with мне удалось + infinitive, there is no normal subject like я. So Russian uses the default neuter singular form:

• удалось

This is very common in impersonal expressions:

• Мне повезло = I was lucky
• Мне удалось = I managed
• Мне не спалось = I couldn’t sleep

So the neuter form does not mean anything is literally neuter here; it is just the standard form for this kind of structure.

Попасть here means to get into / to make it to / to gain entry to.

That makes it especially suitable for places or events where the important idea is successful access:

• попасть на концерт = get to / get into the concert
• попасть на выставку = get to / get into the exhibition
• попасть в музей = get into the museum

Compared with other verbs:

• идти = to go, to be going
• ходить = to go regularly / on foot / habitually
• прийти = to arrive
• попасть = to manage to get in / get there successfully

So here попасть fits well because the sentence is about successfully getting to the exhibition, especially for free.

Because на can take different cases depending on the meaning.

Here there is movement toward a destination, so Russian uses:

• на + accusative

That gives:

• на выставку = to the exhibition

If you were talking about being located there, Russian would use:

• на + prepositional

For example:

• Я был на выставке = I was at the exhibition

So the contrast is:

• попасть на выставку = get to the exhibition
• быть на выставке = be at the exhibition

Because it describes how the action happened: the speaker got in for free.

So бесплатно works like an adverb:

• попасть бесплатно = to get in for free

Russian often uses бесплатно exactly this way:

• войти бесплатно = enter for free
• учиться бесплатно = study for free
• получить билет бесплатно = get a ticket for free

An adjective would need to describe a noun, for example:

• бесплатный билет = a free ticket
• бесплатный вход = free entry

But in your sentence, the word modifies the action, not a noun, so бесплатно is the correct choice.

Yes. Russian word order is flexible, and бесплатно can move around.

For example:

• Мне удалось попасть на выставку бесплатно.
• Мне удалось бесплатно попасть на выставку.

Both are natural.

Very roughly:

• попасть на выставку бесплатно puts for free after the destination and sounds neutral
• бесплатно попасть на выставку highlights the idea of doing it for free a bit earlier

Russian word order often changes focus rather than basic meaning.

Both can mean that the person got to the exhibition, but the emphasis is different.

• Я попал на выставку = I got to / got into the exhibition
• Мне удалось попасть на выставку = I managed to get to / get into the exhibition

The version with удалось highlights the fact that this was an achievement or a successful outcome.

So:

• Я попал на выставку бесплатно is a straightforward fact
• Мне удалось попасть на выставку бесплатно suggests success, maybe against some difficulty

In many situations, the second one feels more expressive.

Yes, often there is.

Удалось frequently implies one or more of these ideas:

• it was not easy
• it was uncertain
• there was some obstacle
• things worked out successfully

It does not always mean pure luck, but it often suggests more than simple ability.

For example:

• Мне удалось найти врача. = I managed to find a doctor.
• Нам удалось купить билеты. = We managed to buy tickets.

These sentences sound like the result was achieved, perhaps after some effort or despite possible problems.

You would normally say войти на выставку? No — that combination is not the best.

With войти, Russian usually uses в / во + accusative when talking about entering a physical space:

• войти в музей
• войти в зал
• войти в здание

But for events and many public venues, попасть на выставку is especially natural.

So the most idiomatic choice here is:

• Мне удалось попасть на выставку бесплатно.

You might also hear:

• Мне удалось бесплатно пройти на выставку.

Here пройти на выставку can suggest being let in, passing through entrance control, or entering successfully.

Either is possible. Russian has no articles, so выставку by itself does not tell you whether English should use the or an.

The choice depends on context:

• if both speaker and listener know which exhibition is meant, English would often use the exhibition
• if it is being mentioned for the first time or is not specific, English might use an exhibition

So Russian leaves that detail to context.

Not necessarily. The sentence means that the speaker got in for free.

That could happen in different ways:

• the exhibition had free admission
• the speaker got a free pass
• the speaker was let in without paying
• there was some special opportunity

So бесплатно tells you about the result for the speaker, not the general admission policy by itself.

If you specifically wanted to say that the exhibition was free for everyone, Russian would often say something like:

• Вход на выставку был бесплатным. = Admission to the exhibition was free.

Because the construction is impersonal.

The main finite verb is удалось, and in this pattern Russian does not use a normal subject like я. Instead, the person involved appears in the dative:

• мне
• тебе
• ему
• нам

So the sentence structure is basically:

• [person in dative] + удалось + infinitive

For example:

• Мне удалось понять. = I managed to understand.
• Ему удалось выиграть. = He managed to win.
• Нам удалось договориться. = We managed to reach an agreement.

This is a very common Russian pattern, even though it feels less direct than English.