Final answer:
Presidents can act without congressional approval through executive agreements, such as the Iran nuclear deal, and signing statements, which interpret and sometimes challenge legislative provisions like those used by President George W. Bush.
Step-by-step explanation:
One example of how the president has acted without the approval of Congress is through the use of executive agreements. An executive agreement is a pact made by the President with the head of a foreign government, which does not require the Senate's approval, unlike formal treaties. A notable example of an executive agreement is the Iran nuclear deal, formally known as the Joint Comprehensive Plan of Action (JCPOA), which was an agreement between Iran and the P5+1 (the five permanent members of the UN Security Council plus Germany) that the Obama administration entered without seeking Congressional approval.
Presidential action without congressional approval can also be seen through signing statements. These are statements issued by the president upon signing the legislation, indicating how the chief executive will interpret and enforce the law, at times challenging congressional intent or provisions of appropriations bills. President George W. Bush famously used signing statements to challenge legislative provisions, such as requirements for reporting on federally funded research.