Uh-huh.
A republic is a state in which the supreme power rests in the body of citizens entitled to vote and is exercised by representatives chosen directly or indirectly by them, according to dictionary.com
Here is the definition of democracy:
Government by the people; a form of government in which the supreme power is vested in the people and exercised directly by them or by their elected agents under a free electoral system.
The burden of proof is on you to show that those two expressly conflict, especially given the fact that most nation-states call themselves 'democratic republics'.
Methinks you should go back to civics class.