How do alliances empire become more powerful. !

By joining with other nations they can receive support so that if an empire is ever in need, or is in a battle with another nation the allies can help the empire. A strong empire is one that has ties with other nations. 

Through this alliances for example the Aztec gained lands, trading connection, and wealth which is the main key that helps the empire became more powerful. In another words, Aztecs had more soldiers, weapons, resources, etc. to be able to conquest other lands with the help of alliances. Furthermore, they also had an advantage of strategy to be able to that and two heads put together is better than one. Relate to this ,Cortes who know as the one who destroys the greatest ancient civilizations( Aztec )with the help of the alliances who were the enemies of Aztec. Today, with the help of alliances and support, U.S.A. became one of the most powerful country in the world. Hope it help!