I was hoping someone could help me with this question. I can't seem to figure out how to simplify it.

The answer is I belive 2p^4 * q^5.

I am working on a clear step by step solution,

( pq^3)^3 (4p^2q)^2

________________                using  (a^m)^n   =  a^(m * n)....so we have

     (2pq^2)^3

(p^3 * q^9) (4^2 * p^4 * q^2 )

_______________________

  ( 2^3 * p^3 * q^6)

( p^3 * q^9 * 16  * p^4  * q^2)

________________________         using  a^m * a^n  =  a^(m + n)

   (8 * p^3 * q^6)

16 *p^7 * q^11

_____________           using    a^m / a^n   =  a^(m - n)

     8 * p^3 * q^6 

2 * p^4 * q^5          just as Coldplay found   !!!!!

CPhill said it better than I could've. Hope it helped!