Entertainment franchises and intellectual properties expand across different mediums by leveraging their existing fan base and brand recognition. This can be achieved through strategic partnerships with production companies, game developers, and merchandise manufacturers to create adaptations in various forms. Additionally, effective marketing campaigns and cross-promotions can help to introduce the franchise to new audiences in different mediums. Overall, a successful expansion involves maintaining the core essence of the franchise while adapting it creatively to suit the characteristics and requirements of each medium.