Ohne seine Brille kann der Student die kleine Schrift kaum lesen.

Breakdown of Ohne seine Brille kann der Student die kleine Schrift kaum lesen.

klein
small
lesen
to read
können
can
sein
his
ohne
without
der Student
the student
die Brille
the glasses
kaum
hardly
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Questions & Answers about Ohne seine Brille kann der Student die kleine Schrift kaum lesen.

Why is it seine Brille and not seiner Brille after ohne?
Because ohne is one of the German prepositions that always takes the accusative case. To form the accusative of a feminine noun with a possessive pronoun, you use the weak declension ending -e (the same as the nominative). If ohne took dative, you would need seiner Brille, but ohne never governs the dative.
Do you need another article before seine Brille, like die or eine?
No. A possessive pronoun (here seine) replaces any article. You wouldn’t say die seine Brille or eine seine Brille, because seine already functions as the determiner.
Why is the finite verb kann in second position even though the sentence begins with Ohne seine Brille?
German main clauses follow the V2 (verb-second) rule: the finite verb must be the second “slot.” Here, the prepositional phrase Ohne seine Brille fills the first slot, so kann comes immediately after, in slot two.
Why is lesen at the very end of the clause?
Because when you use a modal verb like kann, the main verb (lesen) appears as an infinitive at the end of the clause. This is standard verb‐cluster word order in German.
What role does kaum play, and why is it positioned just before lesen?
kaum is an adverb of degree meaning “hardly” or “barely.” In a verb‐cluster (here kann … lesen), degree adverbs typically appear directly before the infinitive to modify that action: kaum lesen = “hardly read.”
Why is der Student in the nominative case while die kleine Schrift is in the accusative?
der Student is the subject of the sentence (the one doing the action), so it takes the nominative. die kleine Schrift is the direct object (the thing being read), so it takes the accusative.
Why does the adjective kleine end in -e in die kleine Schrift?
This is an attributive adjective following a definite article. For feminine singular nouns in the accusative, the weak adjective ending is -e, hence kleine.
How does the word order change if you turn this into a subordinate clause with dass or wenn?

In subordinate clauses introduced by dass or wenn, the finite verb moves to the end of the clause. For example with dass:
  Ich weiß, dass der Student ohne seine Brille die kleine Schrift kaum lesen kann.
Here kann closes the subordinate clause.
With wenn you could say:
  Wenn der Student ohne seine Brille ist, kann er die kleine Schrift kaum lesen.
Notes: In the wenn-clause, ist goes to the end; kann remains in second position of the main clause.

What difference would replacing kaum with nicht make?

kaum means “hardly” or “barely,” implying he can do it but with great difficulty. If you use nicht, you simply negate the ability:
  Ohne seine Brille kann der Student die kleine Schrift nicht lesen.
This means “he can’t read it at all,” which is stronger than “he can hardly read it.”

How can you use a zu-infinitive after ohne, for example ohne seine Brille aufzusetzen, and how does that affect word order?

You can form an infinitive clause with zu to express “without doing something.” For example:
  Ohne seine Brille aufzusetzen, kann der Student die kleine Schrift kaum lesen.
The structure ohne + [NP] + zu + Infinitiv acts as your introductory phrase. The finite verb kann still occupies the second position, and the main infinitive lesen remains at the end.