how many types of assemblies are there?
Curiate Assembly, the Centuriate Assembly, and the Tribal Assembly.
Constitution of the Roman Republic
Roman citizens were organized into three types of voting units: "curiae", "centuria", and "tribus" or tribes. These corresponded to three different kinds of assemblies: the Curiate Assembly, the Centuriate Assembly, and the Tribal Assembly. 
what was the most powerful lawmaking body in the roman republic Assemblies
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Constitution of the Roman Republic [SEP] Assembly types
Roman citizens were organized into three types of voting units: "curiae", "centuria", and "tribus" or tribes. These corresponded to three different kinds of assemblies: the Curiate Assembly, the Centuriate Assembly, and the Tribal Assembly. Each unit (curia, century or tribe) cast one vote before their assembly. The majority of individual votes in any century, tribe, or curia decided how that unit voted. The Curiate assembly () traditionally dates to the early monarchy, from 30 divisions of the city made by Romulus. By the middle Republic, it served only a symbolic purpose. At some point, the 30 "curiae" ceased to actually meet and were instead represented by 30 lictors.