Bursdagskaken er i kjøleskapet.

Norwegian very often makes compound nouns where English uses two or more words.

• bursdag = birthday
• kake = cake
• bursdagskake = birthday cake

The -s- in the middle is a common linking sound in compounds. It does not usually have a separate meaning here; it just helps the word flow naturally.

Then bursdagskaken is the definite form: the birthday cake.

Because Norwegian usually adds the definite article to the end of the noun instead of putting a separate word like the in front.

• en bursdagskake = a birthday cake
• bursdagskaken = the birthday cake

This noun is an en-word (common gender), so the definite ending is -en.

For the same reason: it is in the definite form.

• et kjøleskap = a refrigerator / a fridge
• kjøleskapet = the refrigerator / the fridge

This noun is an et-word (neuter), so the definite ending is -et.

Norwegian often uses the definite form when talking about a specific thing that both speaker and listener can identify.

So this sentence is talking about:

• the birthday cake — a specific cake
• the fridge — a specific fridge, probably the one in the house

This is very natural in Norwegian, just as it is in English in a sentence like The birthday cake is in the fridge.

er is the present tense of å være = to be.

• er = is / are / am

i is the preposition in.

So:

• er i = is in

This is the normal Norwegian word order for a simple statement:

subject + verb + other information

Here:

• Bursdagskaken = subject
• er = verb
• i kjøleskapet = prepositional phrase

So the structure is very similar to English:

• The birthday cake
  • is
    • in the fridge

Yes, you often can, and it may sound very natural.

Norwegian sometimes uses position verbs where English often just uses to be:

• står = stands
• ligger = lies
• sitter = sits

A cake in a fridge is often said to stå i kjøleskapet if it is upright on a shelf or table-like surface.

But er i kjøleskapet is completely correct and neutral. It simply says where it is, without focusing on position.

A few pronunciation points may help:

• kj in kjøleskapet is a soft sound that English does not really have.
• ø is also a vowel English does not have.
• sk before some front vowels can sound like sh, but in skap it is a normal sk sound.

Roughly:

• bursdagskaken ≈ BURS-dahgs-kah-ken
• kjøleskapet ≈ something like HYUR-leh-skah-pet, though that is only an approximation

The hardest part for many learners is kjø. It is best learned by listening to native audio and copying it.

They are:

• en bursdagskake → common gender
• et kjøleskap → neuter

That matters because the indefinite articles and definite endings change:

• en ... / ...-en
• et ... / ...-et

So:

• en bursdagskake → bursdagskaken
• et kjøleskap → kjøleskapet

Yes, i kjøleskapet is the normal and correct phrase for in the fridge.

• i = in
• kjøleskapet = the fridge

You might also hear the shorter everyday word kjølern in very informal speech in some dialects, but kjøleskapet is the standard written form.

Yes. That means The cake is in the fridge.

The difference is that kaken is less specific than bursdagskaken. If the context already makes it clear that the cake is a birthday cake, then kaken is perfectly natural.

Compare:

• Kaken er i kjøleskapet. = The cake is in the fridge.
• Bursdagskaken er i kjøleskapet. = The birthday cake is in the fridge.

The dictionary forms are the indefinite singular forms:

• bursdagskake
• kjøleskap

You would usually learn them with their articles:

• en bursdagskake
• et kjøleskap

That helps you remember the gender and makes it easier to form the definite versions later.