Briefly explain one similarity in the practice of realpolitik by louis napoleon and otto von bismarck.

Both Napoleon III and Otto von Bismarck allowed room for liberal or popular policies that would help them strengthen the government's standing with the people.

Charles-Louis-Napoleon Bonaparte was president of France from 1848-1852, and then Emperor of the French from 1852-1870.  From 1852-1860 he ruled in strongly authoritarian fashion.  But during the period known as the "liberal empire" (1860-1870), in order to shore up popularity for his government, he allowed the legislature more of a role in governing, relaxed censorship of the press, and restored freedom of assembly.  All of these were liberal measures, but politically realistic moves to keep Napoleon III from losing standing with the populace.

Otto von Bismarck, Chancellor of the German Empire from 1871-1890, was not himself a socialist.  But he is famed for introducing the first government programs for social welfare in the Western world.  Socialism had the potential of fomenting revolution among the working class in Germany.  Employing some government measures to respond to the needs and issues of ordinary German workers was a Realpolitik measure.

"teotihuacan was the cultural center of the zapotecs".

They made a checks and balance system to equal power within the branches. the "check" meant that one branch would watch one branch and "balance" them if they were too powerful. if you want more info on this, i would just google checks and balance system.