El profesor exige que pongamos los libros en la mesa.

Questions & Answers about El profesor exige que pongamos los libros en la mesa.

Why is it pongamos and not ponemos?
Because the teacher is making a demand (exige que). Verbs of influence or demand like exigir (to demand) trigger the subjunctive mood in the second part of the sentence. So, the normal indicative ponemos must become the subjunctive pongamos.
How do we get the subjunctive form pongamos from the verb poner?
For verbs with an irregular yo form, the present subjunctive takes that exact same stem. The present indicative yo form of poner is pongo. We drop the -o to get the stem pong-, then add the "opposite" vowel endings. Since poner is an -er verb, the nosotros subjunctive ending is -amos, which gives us pongamos.
Is exige always followed by que?
It depends on what you are demanding. When you demand that someone else do something (like putting books on a table), you use exigir que followed by the subjunctive. If you are just demanding a thing, you skip the que and use a noun directly, such as: El profesor exige respeto (The teacher demands respect).
Could I say sobre la mesa instead of en la mesa?
Absolutely. The preposition en is the most common way to say both "in" and "on" in Spanish, so it sounds perfectly natural here. If you want to be extra specific and emphasize that the books go on top of the table, sobre la mesa is also a great choice.

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