Which of the following is the primary state agency responsible for regulating barbers in Alaska?

The primary state agency responsible for regulating barbers in Alaska is the Alaska Board of Barbers and Hairdressers. This board oversees the licensing and regulation of barbering and hairdressing practices within the state to ensure compliance with health and safety standards. It is tasked with setting educational requirements, conducting examinations for licensing, and enforcing regulations that govern the profession, thereby protecting consumers and maintaining professional standards in the beauty industry.

The other options presented do relate to hair and beauty services in various capacities, but they do not hold the specific authority dedicated to barbers in Alaska. For instance, while an organization like the Alaska State Barber Association may advocate for barbers' interests, it does not have regulatory powers. Similarly, the Alaska Board of Hairdressers primarily focuses on hairdressing and may not cover the specific nuances of barber training and regulation. The Alaska Department of Professional Licensing oversees multiple professions but is not the specialized body focused solely on barbers, making the Board of Barbers and Hairdressers the correct answer for this question.