The readings don't really line up perfectly, but they're close (although mixed in terms of what has what reading). Take a look at the word and break everything down. 浮 takes the kun'yomi うき (from 浮く), 世 also takes the kun'yomi よ, and then 絵 takes the on'yomi え. Put that all together and you have うきよえ! Or if you already know the word ukiyo-e, that works too!
Why don’t we talk about the ukiyo-e?