Wives = 7^1
Sacks = 7^2
Cats = 7^3
Kits = 7^4
Exponents are used when we find the area of a shape, used in banking for finding compounding interest, and used to describe very large and very small numbers. (They are used for many other things, of course, but I don't think you want that kind of list)
You can use exponents to write numbers by writing the exponent for the number of times you are multiplying the base.