How are stereotyping and gender inequality related to each other?
These two are related because they feed upon one another.
Gender inequality helps lead to stereotypes. People see that women are more likely than men to be stay-at-home parents and they create a stereotype that women are naturally made to play this role. These stereotypes, then, lead to further gender inequality. As people come to accept these stereotypes, they are less willing to hire women for good jobs. If women are less able to get hired for good jobs, they are more likely to end up as stay-at-home parents.
This is, then, a vicious cycle in which stereotypes and inequality feed upon and reinforce one another.