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

Assuming that p and q are nonzero, simplify .

\(\dfrac{(pq^3)^3(4p^2q)^2}{(2pq^2)^3}\)

Guest Aug 22, 2018

#1**+1 **

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

I am working on a clear step by step solution,

ColdplayMX
Aug 22, 2018

#2**+1 **

( 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
Aug 22, 2018