Question

Can someone help me with this quick? Thank you!

Answer 1

remember that (ab)/(cd)=(a/c)(b/c)

also remember that
`(a^b)^c=a^(bc)=(a^c)^b`

also,
`(a^b)/(a^c)=a^(b-c)` and
`a^(-b)=(1)/(a^b)` and
`(ab)^c=(a^c)(b^c)`

group the like bits together

`(3(2x^4y^6)^5)/((3x^6y^3)^4)=`

`(3(2^5)((x^4)^5)((y^6)^5))/((3^4)((x^6)^4)((y^3)^4))=`

`((3^1)(2^5)(x^(20))(y^(30)))/((3^4)(x^(24))(y^(12)))=`

`((3^1)/(3^4))((2^5)/(1))((x^(20))/(x^(24)))((y^(30))/(y^(12)))=`

`(3^(1-4))(2^5)(x^(20-24))(y^(30-12))=`

`(3^(-3))(2^5)(x^(-4))(y^(18))=`

`((1)/(3^3))((2^5)/(1))((1)/(x^4))((y^(18))/(1))=`

`((2^5)(y^(18)))/((3^3)(x^4))=`

`(32y^(18))/(27x^4)`