I am doing an exercise. The exercise is telling me to write the dative form of given words or phrase. I am stuck in one place. A phrase is given "Die Leute", and an answer is given in dative form is "Den Leuten". My question is why "Leuten" not "Leute"? I understood why there is "den". But I could not understand why "Leuten". As I know the n declination works only for masculine.
The German noun »Leute« is a plurale tantum. This is the name of a group of nouns, that exist only in plural form. The singular form is not in use. English examples are pants, scissors, genitals. German examples are Ferien, Kosten, Gebrüder. (There are more in both languages, and in other languages too.)
Some centuries ago, in the Middle High German language, the noun »Leute« was »liute«, and it had a singular form with two grammatical genders: »der liut« (masculine) and also »daჳ liut« (neuter). The meaning was the people or the population. So even the singular form didn't mean a single person, but a big group of persons. And because singular and plural meant the same amount, which was many, the singular was not used any longer and became extinct.
If the singular form would have survived, it would be »der Leut« or »das Leut« in modern German, and it would belong to the nouns that are declined strong (strong declension), i.e. similar to »der Weg« or »das Pferd«, and this is why the existing plural really belongs to strong declension:
Singular (extinct! do not use!)
Nom: der/das Leut
Gen: des Leuts/Leutes
Dat: dem Leut
Akk: den/das Leut
Nom: die Leute
Gen: der Leute
Dat: den Leuten
Akk: die Leute