Probably you are ending up with a negative number for Density, which tends to do that sort of thing. Odd powers have the property that negative numbers stay negative, while even powers will always be positive. You can probably make it work by sticking an absolute value in right after the Power node.
In the PRT Volume object there is a pair of spinners that affect the randomness of the particles (RandomCount and RandomSeed). RandomCount is the number of unique random numbers that are used for the pool of particle positions. They can’t be truly random because then the same particles would not be created each time the object was evaluated.
If the RandomCount is too low, obvious patterns will develop. I recommend a minimum of 1024 for this value. What are you currently using?