Federal republic

A federal republic is a republic made up of a number of constituent states, in which the relationship between the federation and the constituent states is governed by the constitution, and cannot be altered without altering that constitution. Governmental powers, including legislative and executive powers and legal jurisdictions, are distributed between the federation and the constituent states. The federation will almost always have the powers relating to foreign policy and defence, but may have much more besides. The balance of powers between the federation and the constituent states helps to determine the character of the republic. One of the most important factors in that balance is the location of the residual powers, that is, those powers not specifically allocated by the constitution. The federal constitution may also lay down the constitution of the constituent states, or each of those states may determine its own constitution.

Some notable federal republics
Germany

India

Russia

Switzerland (one of the oldest)

United States of America

Australia and Canada generally conform to the model, but are technically constitutional monarchies, not republics.