which language was spoken by the people of that time?
Nahuatl language
Language and placenames
Nahuatl language 
the culture of the aztec empire was based around which geographic form Central Mexico this culture became popular between which time period? Post-classic period from 1300 to 1521
Nahuatl. Nahuatl Nahuatl language
Aztecs Aztecs Aztecs
Introduction Language and placenames Language and placenames
 The Aztec peoples included different ethnic groups of central Mexico, particularly those groups who spoke the Nahuatl language and who dominated large parts of Mesoamerica from the 14th to the 16th centuries.  The Nahuatl language is today spoken by people, mostly in mountainous areas in the states of central Mexico. Mexican Spanish today incorporates hundreds of loans from Nahuatl, and many of these words have passed into general Spanish use, and further into other world languages. The Nahuatl language is today spoken by people, mostly in mountainous areas in the states of central Mexico. Mexican Spanish today incorporates hundreds of loans from Nahuatl, and many of these words have passed into general Spanish use, and further into other world languages.
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Aztecs [SEP] Language and placenames
The Nahuatl language is today spoken by people, mostly in mountainous areas in the states of central Mexico. Mexican Spanish today incorporates hundreds of loans from Nahuatl, and many of these words have passed into general Spanish use, and further into other world languages. In Mexico, Aztec place names are ubiquitous, particularly in central Mexico where the Aztec empire was centered, but also in other regions where many towns, cities and regions were established under their Nahuatl names, as Aztec auxiliary troops accompanied the Spanish colonizers on the early expeditions that mapped New Spain. In this way even towns, that were not originally Nahuatl speaking came to be known by their Nahuatl names.