ryokou no ato, ie ni buzi ni kaerimasita.

Japanese often leaves out the subject when it is clear from context.

So 旅行のあと、家に無事に帰りました。 naturally means something like After the trip, (I/we/he/she) returned home safely, depending on the situation.

In many everyday sentences, Japanese does not state 私, 彼, 彼女, etc. unless it is needed for clarity or emphasis.

旅行 means trip/travel, and あと means after.

The pattern here is:

noun + の + あと = after noun

So:

• 旅行のあと = after the trip
• 授業のあと = after class
• 食事のあと = after the meal

The の connects the noun 旅行 to あと.

The の links one noun to another.

Here, あと is being treated like a noun meaning the time after something. So 旅行のあと literally works like the trip’s after, or more naturally, after the trip.

This is a very common pattern in Japanese:

• 映画のあと = after the movie
• 仕事のあと = after work
• 学校のあと = after school

The comma marks a pause and separates the time expression from the main action.

So the sentence is structured like:

• 旅行のあと、 = After the trip,
• 家に無事に帰りました。 = returned home safely.

Japanese commas are often used more flexibly than English commas, but here it helps show that 旅行のあと is setting the time frame for the rest of the sentence.

In this sentence, に marks the destination of movement.

So:

• 家に帰る = to return home
• 学校に行く = to go to school
• 日本に来る = to come to Japan

Here, 家に means to home / homeward in grammatical terms, but in natural English we just say home.

With verbs of movement like 行く, 来る, and 帰る, に often marks the place you are going to.

Yes, 家へ帰りました is also possible.

Both に and へ can mark direction/destination with movement verbs, but there is a slight nuance:

• に focuses more on the destination
• へ focuses more on the direction toward that place

In many everyday sentences, especially with 帰る, に is very common.

So:

• 家に帰りました = returned home
• 家へ帰りました = went/returned toward home

In practice, both can often be translated the same way.

無事 means safety, without trouble, or safe/unharmed depending on context.

In this sentence, 無事に works as an adverb meaning:

• safely
• without incident
• all right

The に turns it into an adverbial expression.

So:

• 無事に帰りました = returned safely
• 無事に着きました = arrived safely

This is similar to how many na-adjectives or noun-like words become adverbial with に.

It behaves like a na-adjective and can also act in noun-like ways.

For example:

• 無事な旅行 = a safe trip
• 無事です = is safe / is all right
• 無事に帰る = return safely

So in 無事に帰りました, it is being used adverbially.

This is why learners often see it described in different ways depending on the dictionary or textbook.

帰る specifically means to return or to go back to a place one belongs, such as home.

So:

• 行く = go
• 来る = come
• 帰る = return/go home

Because the sentence says 家に and the meaning is returning home after a trip, 帰りました is the natural verb.

Examples:

• 学校に行きました = went to school
• 日本に来ました = came to Japan
• 家に帰りました = went home / returned home

The dictionary form is 帰る.

The polite non-past form is:

• 帰ります

The polite past form is:

• 帰りました

Since the sentence describes a completed action, it uses past tense.

So:

• 帰ります = return / will return
• 帰りました = returned

The -ました ending is the standard polite past form.

In this sentence, 家 means home/house, and in the expression 家に帰る, it is very often understood as うち in everyday speech, though いえ is also possible depending on context and speaker.

A useful learner point is this:

• いえ often refers more literally to a house/building
• うち often means home, my place, or our place

But in fixed expressions like 家に帰る, the exact reading is not always the main issue for beginners. What matters most is that the phrase means to go/return home.

Yes. 旅行のあとで、家に無事に帰りました。 is also possible.

Both あと and あとで can mean after, but あとで often sounds a little more explicitly like after that or later, after...

In this sentence:

• 旅行のあと、 = after the trip
• 旅行のあとで、 = after the trip / after that

Both are natural, though 旅行のあと、 is very straightforward and common.

Both are possible.

• 家に無事に帰りました
• 無事に家に帰りました

Japanese word order is more flexible than English as long as the particles make the roles clear.

The sentence you were given places the destination first, then the manner:

• 家に = home
• 無事に = safely
• 帰りました = returned

But 無事に家に帰りました is also very natural and may sound a little more like safely made it home.

It most naturally means returned home after a trip.

Because the sentence begins with 旅行のあと and uses 帰りました, the overall feeling is that the speaker was away on a trip and then came back home safely.

So the nuance is not just random movement. It is specifically a safe return after being away.

A simple breakdown is:

旅行のあと、家に無事に帰りました。

• 旅行 = trip
• の = linking particle
• あと = after
• 家に = to home
• 無事に = safely
• 帰りました = returned

So the pattern is:

[time expression], [destination] [manner] [verb]

That is a very common Japanese sentence structure.