فرشاة الأسنان ومعجون الأسنان على الطاولة.

Because Arabic often leaves out the verb to be in the present tense.

So فرشاة الأسنان ومعجون الأسنان على الطاولة is a normal present-tense nominal sentence meaning something like:

• The toothbrush and the toothpaste are on the table.

In Arabic, you do not need a separate word for are here.
If you wanted the past tense, then Arabic would use a verb, for example:

• كانا على الطاولة = They were on the table (dual)
• or more naturally with the full noun phrase repeated as needed

So in this sentence, the structure is basically:

• subject: فرشاة الأسنان ومعجون الأسنان
• predicate/location: على الطاولة

Both are examples of the iḍāfa construction, often called the construct phrase.

That means:

• فرشاة الأسنان = literally brush of the teeth
• معجون الأسنان = literally paste of the teeth

This is how Arabic commonly expresses noun combinations that English often makes into one word or an adjective+noun phrase:

• toothbrush = brush of the teeth
• toothpaste = paste of the teeth

In an iḍāfa:

1. the first noun comes first
2. the second noun specifies it
3. the second noun is in the genitive
4. the first noun does not take الـ if it is part of this structure

So Arabic says فرشاة الأسنان, not الفرشاة الأسنان in this sentence.

Because each noun phrase is separate:

• فرشاة الأسنان = toothbrush
• معجون الأسنان = toothpaste

English sometimes avoids repetition more easily, but Arabic usually repeats the full iḍāfa phrase when the two items are separate nouns.

If you said only one الأسنان, that would not clearly give both nouns their own full expression. Repeating it is the normal and clear way to say it.

In an iḍāfa construction, the first noun usually does not take الـ.
Its definiteness is determined by the second noun.

Since الأسنان is definite (the teeth), the whole phrase فرشاة الأسنان becomes definite:

• فرشاة الأسنان = the toothbrush
• معجون الأسنان = the toothpaste

This is a very important Arabic pattern:

• باب البيت = the door of the house / the house door
• not الباب البيت

So even without الـ on فرشاة, the whole phrase can still be definite.

Arabic commonly uses teeth in these expressions:

• فرشاة الأسنان = toothbrush
• معجون الأسنان = toothpaste

Literally this is more like brush of the teeth and paste of the teeth.

Languages do not always match English word-for-word. English uses tooth- in the singular in compounds, but Arabic uses الأسنان (the teeth) in these standard expressions.

So this is something to learn as a set phrase, not by translating each part too literally.

و means and.

Arabic writes many short particles attached directly to the following word, and و is one of them. So:

• ومعجون = and toothpaste

This is completely normal Arabic spelling.
It is not a separate spacing mistake; it is supposed to be attached.

So the sentence has two coordinated nouns:

• فرشاة الأسنان
• ومعجون الأسنان

Together: the toothbrush and the toothpaste

على means on, and الطاولة means the table.

Together:

• على الطاولة = on the table

This whole prepositional phrase acts as the predicate of the sentence, telling you the location of the subject.

So the sentence structure is:

• فرشاة الأسنان ومعجون الأسنان = the toothbrush and the toothpaste
• على الطاولة = on the table

Arabic often puts location phrases like this after the subject, just as English often does.

Yes. Arabic word order is more flexible than English.

You can say:

• فرشاة الأسنان ومعجون الأسنان على الطاولة
• على الطاولة فرشاة الأسنان ومعجون الأسنان

Both are grammatical. The second version puts more focus on the location first, something like:

• On the table are the toothbrush and the toothpaste.

The original order is straightforward and very natural.

A fully vowelled version would be:

فُرْشَاةُ الْأَسْنَانِ وَمَعْجُونُ الْأَسْنَانِ عَلَى الطَّاوِلَةِ

The case endings are:

• فُرْشَاةُ — nominative, because it is part of the subject
• الْأَسْنَانِ — genitive, because it is the second term of the iḍāfa
• مَعْجُونُ — nominative, coordinated with the first noun phrase
• الْأَسْنَانِ — genitive again, for the same reason
• الطَّاوِلَةِ — genitive, because it comes after the preposition على

In normal unvowelled writing, these endings are usually not shown.

Yes—here the final ة in فرشاة is pronounced as t, because the word is in an iḍāfa construction and is followed directly by another noun.

So you would pronounce it roughly like:

• furshat al-asnān

not just furshāh in this context.

This is a common rule with taaʾ marbūṭa:

• at pause, it often sounds like -ah
• before another word in connected speech, especially in grammar like iḍāfa, it is often pronounced -at

The same idea applies whenever a taaʾ marbūṭa is grammatically “active” in connected speech.

It can be a complete sentence in MSA.

Because Arabic allows present-tense nominal sentences without is/are, this is a full sentence meaning:

• The toothbrush and the toothpaste are on the table.

At the same time, without context, it could also look a bit like a simple descriptive line or a caption, since Arabic often uses short verbless structures in labels, instructions, and picture descriptions.

So grammatically it works as a sentence, but stylistically it could also fit a caption-like context.