To which branch of government does the power to interpret laws and apply the constitution to the law belong? federal executive judicial legislative

The power to interpret laws and apply the Constitution to the law belongs to the judicial branch of government.
The judicial branch is there to analyze the laws created by the legislative branch and decide what should be done about them. The executive branch has to do with the actual implementation of the law - so if someone breaks the law, the executive branch will have to take action to remedy that.