Final answer:
An agency relationship formed through an explicit oral or written contract between principal and agent is an express agency, which is distinct from implied and dual agencies, as well as a power of attorney.
Step-by-step explanation:
When a principal and an agent enter into an agreement through an oral or written contract that explicitly states the authority and obligations of the agent, this type of relationship is known as an express agency. This is in contrast to an implied agency, which is formed by the actions and circumstances rather than a formal agreement, and a dual agency, where an agent acts for two principals simultaneously in a transaction. Power of attorney is a document that grants an individual the authority to act on behalf of another in legal or financial matters, but it is not the correct answer to the question about types of agency relationships.