I am not exactly sure what it is trying to say. So if you do know please leave a comment. But what I think it means is that in the example 5^-2. 5 is squared by -2. It is that number out of 1. I would do 5*5 which is 25. I would then put 1 over 25. I think that this is how you are supposed to be solving this equations. We have not yet talked about this in Algebra so I do not guarantee that this is the best way to do it, but it still works so for know this the solution that I use. If there is a better way to do it, please let me know in the comments.
 
Exponents are just an easier way of writing multiplactin. For example, if it 5 squared by 10. 5 squared by 10 is just an easier way of writing 5*5*5*5*5*5*5*5*5*5. We use exponents because we are lazy. We choose not to write all of it, so we just square it instead of writing 5*5*5*5*5*5*5*5*5*5. We use exponents to save time. We use exponents when we are talking about how much land there is. It could be 16 feet squared. 16 feet squared is 256 feet. Instead of 16*16 we do 16 feet squared.