Which clause ensures that laws are applied equally across different persons and circumstances?

The correct choice is the Equal Protection Clause, which is part of the Fourteenth Amendment to the U.S. Constitution. This clause is specifically designed to ensure that individuals are treated equally under the law, prohibiting states from discriminating against individuals based on race, gender, or other statuses. The principle behind the Equal Protection Clause is that all people should receive the same legal protections and treatment, ensuring fairness in the application of laws across different persons and circumstances.

The Due Process Clause, while also significant, primarily focuses on the guarantee that legal proceedings must be fair and that individuals cannot be deprived of life, liberty, or property without appropriate legal processes. It does not directly address equal treatment in the same way that the Equal Protection Clause does.

The Privileges and Immunities Clause prevents states from discriminating against citizens of other states in favor of its own citizens but is more focused on interstate relations and does not cover all equal treatment issues.

The Commerce Clause grants Congress the power to regulate commerce among the states, which is unrelated to the equality of laws as applied to individuals.

Thus, the Equal Protection Clause distinctly ensures that laws are applied equally, making it the correct answer.