The US Constitution manifests the principle of a republican form of government because it allows US citizens over the age of 18 to vote. A republican government is one in which the power of the government comes from the citizens. The US Constitution allows the US to be a republican form of government, as the citizens pick who is in office.
The US Constitution manifests the principle of a democratic form of government because it allows citizens to pick leaders who will make rules for their state/country. Citizens have the ability to pick who will serve in Congress and who will be president. These leaders then make laws for the country to follow.