Purity, well, you could have power over marriage, virginity, cleanliness (good for water, curative properties, etcetera), babies, etcetera. 

With Beauty, well that could include both hot babes, hot dudes, or metaphorical beauty. (It's on the inside that counts). Or even just shiny things. 

With powers over knowledge, you could automatically receive information in your mind without trying to learn anything. Not necessarily prophetic things that let you know things in the future, but you might be able to mathematically theorize correctly what would happen in a certain amount of time with a high degree of accuracy.

With wisdom, you would be able to know many answers about life, awareness of the things around you in intimate detail, etcetera, know how to bring about positive change, etcetera.