Final answer:
The necessary and proper clause of Article I, Section 8, has been most frequently used to expand the national government's power by allowing the development of implied powers beyond those enumerated. The supremacy clause reinforces this by asserting federal supremacy over state laws.
Step-by-step explanation:
The Constitutional clause that has been used most often to expand the power of the national government is the necessary and proper clause, also known as the elastic clause, which is found in Article I, Section 8.
This clause grants Congress the authority to make all laws which shall be deemed "necessary and proper" for executing its powers. Over time, this has facilitated the expansion of federal power through the development of implied powers, allowing the government to enact legislation on many policy matters, such as healthcare, taxation, and the regulation of interstate commerce, that go beyond its enumerated powers.
The supremacy clause in Article VI also plays a vital role in expanding federal power by asserting that the Constitution and federal laws override state laws and constitutions in case of conflict. Significant cases, such as the McCulloch decision, established the doctrine of implied powers and confirmed the principle of national supremacy, reflecting the power dynamics set by the Constitution between the national and state governments.