What term refers to a state Administrator's power to review records within and outside the state?

The term that refers to a state Administrator's power to review records within and outside the state is "Inspectorial powers." This term is specifically used to describe the authority granted to state regulators or administrators to examine, inspect, and investigate activities of financial organizations and professionals to ensure compliance with state laws and regulations. The inspectorial powers allow the administrator to scrutinize records, documents, and conduct inquiries, both within the state and possibly extending to other jurisdictions, as needed for effective regulation and enforcement.

This function is critical because it helps maintain the integrity of the financial systems and protects investors and consumers from fraudulent activities or mismanagement. While terms like regulatory jurisdiction, compliance authority, and audit capabilities may involve aspects of oversight or inspection, "inspectorial powers" most accurately encapsulates the specific authority to look into records and practices as part of regulatory enforcement.