Negative exponents are basically abbreviations for big ugly fractions. In the same way that it's quicker to write LMAO in place of the longer version, negative exponents will make it much easier to text all your friends about algebra. We know that's what 95% of all your texts are about. You're so obsessed.
Let's start with a simple example that showcases the additive rule:
In other words, 
is the multiplicative inverse or reciprocal of 
. Therefore, 
. Got that, Fraction Jackson?
Sample Problems
, that is, 
, is the reciprocal of 
.
means 
.
Make sure you put negative exponents in that part of your brain where you keep things, right in between the cheat codes for Street Fighter and the fantasy stats for every professional baseball player. They'll be important when you learn scientific notation, which we'll talk about later. You'll need to hang in there and notate stuff unscientifically until then.