Ich trockne das Glas mit dem Handtuch ab.

Because the full verb is abtrocknen, which is a separable verb.

• Dictionary form: abtrocknen
• In a normal main clause, the prefix separates:
  • Ich trockne das Glas mit dem Handtuch ab.

This is very common in German:

• anmachen → Ich mache das Licht an.
• aufstehen → Ich stehe früh auf.

So here, trockne ... ab belongs together and means dry off / dry.

trocknen means to dry in a general sense, while abtrocknen often means to dry something off or wipe it dry, especially after washing.

In this sentence, abtrocknen is the natural choice because you are drying the glass with a towel.

Compare:

• Die Wäsche trocknet. = The laundry is drying.
• Ich trockne die Wäsche. = I dry the laundry.
• Ich trockne das Glas ab. = I dry the glass off / wipe the glass dry.

So abtrocknen often suggests removing moisture from a surface.

Because Glas is a neuter noun: das Glas.

Here it is the direct object of the verb, so it is in the accusative case. But for neuter nouns, the article das stays the same in nominative and accusative:

• Nominative: das Glas
• Accusative: das Glas

So even though it is the object, it still appears as das Glas.

Because the preposition mit always takes the dative case.

Handtuch is also a neuter noun:

• Nominative: das Handtuch
• Dative: dem Handtuch

So:

• mit dem Handtuch = with the towel

This is a very important rule:

• mit dem Auto
• mit der Frau
• mit dem Kind

Whenever you use mit, expect the noun after it to be dative.

In this sentence, it means using the towel as the instrument.

So:

• Ich trockne das Glas mit dem Handtuch ab. = I dry the glass with the towel.

German uses mit for this kind of instrumental meaning very often.

In theory, mit can also mean together with, but here the context and the verb make the meaning clear: the towel is the thing being used to dry the glass.

German main clauses usually put the conjugated verb in second position.

So the structure is:

• Ich = subject
• trockne = conjugated verb in position 2
• das Glas = object
• mit dem Handtuch = prepositional phrase
• ab = separated prefix at the end

That gives:

• Ich trockne das Glas mit dem Handtuch ab.

The middle part can often move around, for example:

• Ich trockne mit dem Handtuch das Glas ab.

But the most natural version is usually:

• Ich trockne das Glas mit dem Handtuch ab.

Yes, you can, and people will understand you.

• Ich trockne das Glas. = I dry the glass.
• Ich trockne das Glas ab. = I dry the glass off / wipe it dry.

The version with ab sounds more complete and natural when you mean removing water from the glass after washing it.

So both are possible, but abtrocknen fits this situation especially well.

Yes. In German, das Glas commonly means a drinking glass.

Depending on context, Glas can also mean:

• glass as a material
• a glass as a container
• sometimes even a jar

But in a sentence like this, das Glas is naturally understood as the drinking glass.

Since abtrocknen is separable, its form changes depending on the tense or structure.

Examples:

• Present: Ich trockne das Glas ab.
• Perfect: Ich habe das Glas abgetrocknet.
• Infinitive: Ich will das Glas abtrocknen.
• Subordinate clause: ..., weil ich das Glas abtrockne.

Notice:

• In the present main clause, the prefix separates: trockne ... ab
• In the perfect participle, it becomes one word: abgetrocknet
• After a modal verb, the infinitive stays together: abtrocknen
• In a subordinate clause, it also stays together at the end: abtrockne

Usually, no. German normally requires the subject pronoun.

So you say:

• Ich trockne das Glas mit dem Handtuch ab.

Not normally just:

• Trockne das Glas mit dem Handtuch ab.

That second version sounds like a command:

• Dry the glass with the towel.

So in normal statements, German usually keeps ich, du, er, and so on.

Yes. The article depends on whether you mean a specific towel or just any towel.

• mit dem Handtuch = with the towel
• mit einem Handtuch = with a towel

Both are correct.

And because mit takes dative, the forms are:

• dem Handtuch
• einem Handtuch

So the case rule stays the same even when the article changes.