There are several different ways that The Arabian Nights, or The Thousand and One Nights, explores, plays off of, and subverts women's roles and stereotypes. One of the main ways that this collection of stories explores power is through the book's frame narrative. The king is angry at women because he discovers his wife having an affair. He has his first wife executed and decides that he will now marry virgins, have sex with them, and then kill them the following morning before they have the chance to be unfaithful to him or hurt him in other ways. This storyline is already one example of a stereotype of masculinity — that of a violent, power-hungry king who uses his power to hurt women.
When he marries Shahrazad, however, she tells him stories each night to keep him interested, prevent him from killing her, and thus save other women in the kingdom from his wrath. This frame narrative suggests the ways in which, in a violent patriarchal world where men seemingly have all the power, women can use language and stories to reclaim power, to survive, to express themselves even when they are silenced, and to create new worlds through these stories where women perhaps have more freedom.
Many of the stories Shahrazad tells feature women who fall into the stereotype of being powerless objects, merely existing for men's pleasure. For example, in the story "The Merchant and His Wife," the merchant beats his wife in order to control her and to keep her from disobeying him. While at first this story seems violent and misogynistic, the context in which this story is told is everything. Shahrazad's father tells her this story towards the beginning of the book in order to try to force her to not marry the king. After listening to this story, Shahrazad disobeys her father and marries the king anyway. Thus, this story exemplifies one of the ways in which this book presents a stereotype of power dynamics between men and women, and then subverts this stereotype by showing us how a woman rebels and refuses to fit in with this particular idea of womanhood.
Many of the stories in this book also explore the stereotype/power dynamic of women as slaves. However, once again, this stereotype is often turned on its head in a way that empowers women. In the story "The Tale of Sympathy the Learned," a young slave girl is extremely intelligent and well-educated and uses this intelligence to empower herself. We could view this story as one that represents Shahrazad's power fantasies and hopes for herself, as the slave girl's use of intelligence to gain power mirrors Shahrazad's storyline with the king.
There are certainly many different stories in Arabian Nights that seem to feature women as powerless individuals subjected to male violence. However, again, it's crucial to look at all of these stories in the context of Shahrazad's frame narrative, in which she is a powerful woman who disobeys her father, seduces/tricks/influences the king, and helps both herself and all the other women in the kingdom survive. Using only her intelligence, persistence, and creativity, Shaharazad ends up influencing the most powerful man in a patriarchal society. Thus, the book's ending suggests that this story is ultimately a story of women's survival, and perhaps even liberation.