This question asks for the definition of police powers. Police powers are powers to regulate health, safety, and wellbeing of citizens. These powers were reserved to the state governments under the Constitution. Executive power is power only exercised by the president in the US or a governor of a state. The legislative power are powers exercised by Congress or a state legislature to write legislation. The judicial power are powers exercised by judges or courts to interpret the law and decide cases. The sovereign power could mean a few things, but most generally it refers to all government's authority to rule, which would encompass police powers as well as all the other things government does.

Under the period of Dual Federalism (1789-1937), state governments retained most of the political authority in the United States. The Federal government's authority was relatively narrow and only applied to those powers explicitly granted to it by the Constitution. After 1937 until the 1960s, the US entered into a period called cooperative federalism where the federal government's power to regulate the economy grew while state powers generally decreased. From 1960 to 1980s, the US entered in a period called regulated federalism where the Federal government began to use its power to force the states to comply with its directives. The Federal government became more powerful than the state governments after 1937. Before 1937, the states generally possessed more authority in domestic affairs than the federal government.

Dual Federalism ended for a variety of related reasons. The only one that isn't true is state governments began to delegate their authority to the federal government. All of the other reasons help explain why Dual Federalism came to an end in the late 1930s. President Franklin Roosevelt and large Democrat majorities in Congress passed a program of laws regulating the American economy called the New Deal which allowed the Federal government to regulate state governments in order to improve the economy. But the president needed the Supreme Court to support his interpretation of the Constitution. The Supreme Court initially resisted the New Deal and overturned some of it as unconstitutional. After 1937, however, the Court began to support New Deal legislation and the government's increased regulations ending dual federalism once and for all. Congress also contributed to the end of dual federalism by vigorously using the “necessary and proper” clause to expand the number of implied powers. Congress used its implied powers to regulate the economy and justify the president's New Deal program.

After the end of Dual Federalism in 1937, the Federal Government continued to expand its authority by relying on grants-in-aid money to the states to encourage state governments to comply with federal standards and programs. From 1937 to the 1960s, the US entered a period called cooperative federalism, where the Federal government would pass laws requiring the state governments to act, but the Federal government would pay any costs on the states. These payments to the states are called grants-in-aid. After the 1960s, the US entered a period called regulated federalism where the Federal government continued to impose regulations or other requirements on the state governments, but it failed to pay the costs that the states incurred by complying. Instead,  the Federal government would fine or penalize states who did not comply with Federal rules and regulations. The Federal government almost never supported local politicians in state elections that would advance federal policy goals once in state office. The president sometimes used the Mass media to pressure state governments but this isn't widespread and it occurred a bit later over issues like civil rights.

When the Federal government imposes a national standard on the state governments without paying the costs for states to adhere to the standard, the federal government imposes an unfunded mandate on the states. Grants-in-aid refers to money that the Federal government pays to the state governments in order to help they comply with Federal rules and regulations. Formula grants are grants where the government uses a precise mathematical formula to determine how much to give to recipients. Ex post facto grants are not a real thing; it is a nonsense answer.

When the Federal government threatens to withhold funds to force states to comply with its priorities, like the national seed limit, the federal government relies on a tactic that characterizes the period of Regulated Federalism. Dual Federalism refers to the period before 1937, where the state and federal power remained separate and in general the states possessed more authority than the federal government. Cooperative federalism refers to the period from 1937 to 1960s where the Federal government uses grants-in-aid to pay the costs for any of its regulations imposed on the State governments. New Federalism refers to a period during the 1980s and 1990s, where Republican presidents and the Supreme Court began to make some reforms to reduce the power of the Federal government over the state governments.

Regulated Federalism refers to the period since the 1960s where the Federal government increasingly set national standards and punished states by withholding grant money for failing to conform to those standards. Dual Federalism refers to the period prior to the 1930s, where states retained most of the political power to regulate the economy and the federal government’s authority was limited to regulating interstate commerce. New Federalism refers to the period mainly under Republican presidents since the 1970s and 1980s whereby the federal government began to loosen some restrictions on state governments, especially the use of unfunded mandate. Cooperative federalism refers to the period from 1930s to the 1960s where the Federal government increasingly set national standards but granted states the money for the costs of meeting those standards.

The correct definition for "Sovereignty" is supreme and independent political authority. "Bicameralism" is the separation of the national legislature into two houses. The separation of powers is when the national government is separated into three different branches--the executive, the legislative, and the judicial branches. "Federalism" is the division of powers and functions between the national government and the state governments.

Under the doctrine of expressed powers and the 10 Amendment, powers not explicitly granted to the national government by the Constitution are reserved to the state governments. Powers not granted to the Federal government under the Constitution or reserved to the states are left to the people under the 9th amendment. Popular sovereignty is the ability of the people to rule in their own right. The US has limited popular sovereignty through state referendums. Most powers or authorities that aren't granted to the Federal government are left to the state governments. Powers that are shared by both the people and the Federal government are called concurrent powers.