How do you evaluate \frac{(2p^{3}q^{4})^{4}}{(-3q^{5})^{2}}\div \frac{(4p^{2}q)^{2}}{9}=\frac{p^{a+b}}{q^{a-b}}?

1 Answer
Dec 15, 2017

b=6
a=2

(p^(a+b))/(q^(a-b))=(p^(2+6))/(q^(2-6))=(p^(8))/(q^(-4))

Explanation:

((2p^3q^4)^4)/((-3q^5)^2)-:((4p^2q)^2)/9=(p^(a+b))/(q^(a-b))

(2^4*p^((3*4))*q^((4*4)) )/((-3)^2*q^((5*2)))*9/(4^2*p^((2*2))*q^2)

(cancel16*p^(12)*q^(16) )/(cancel9*q^(10))*cancel9/(cancel16*p^(4)*q^2)

(p^(12)*q^(16) )/(q^(10))*1/(p^(4)*q^2)

(p^(12)*q^(16) )/(q^(10)*p^(4)*q^2)

(p^(12)*q^(16) )/(q^((10+2))*p^(4))

(p^((12-4)))/(q^((12-16)))=(p^(8))/(q^(-4))

a+b=8
a-b=-4quad=>quada=b-4


b-4+b=8quad=>quad2b=12quad=>quadb=6
a=b-4quad=>quada=6-4quad=>quada=2