Question

Simplify the following exponential expression. Show your work step by step and list the Properties of Exponents used to solve this problem next to your work.

Answer 1

`(3x^0(2x^3y^2)^4)/((4x^7y^4)^2)`

`(3x^0(2x^3y^2)^4)/((4x^7y^4)^2) =(3(1)(2x^3y^2)^4)/((4x^7y^4)^2)` Since,
`a^0=1`

`(3x^0(2x^3y^2)^4)/((4x^7y^4)^2) =(3(2)^4(x^3)^4(y^2)^4)/((4)^2(x^7)^2(y^4)^2)` Since,
`(ab)^m=a^mb^m`

`(3x^0(2x^3y^2)^4)/((4x^7y^4)^2) =(3(16)x^(12)y^(8))/(16x^(14)y^(8))` Since,
`(a^m)^n=a^(mn)`

`(3x^0(2x^3y^2)^4)/((4x^7y^4)^2) =(3x^(12)y^(8))/(x^(14)y^(8))`

`(3x^0(2x^3y^2)^4)/((4x^7y^4)^2) =3x^(12-14)y^(8-8)` Since,
`(a^m)/(a^n) =a^(m-n), a^0=1`

`(3x^0(2x^3y^2)^4)/((4x^7y^4)^2) =3x^(-2)y^(0)`

`(3x^0(2x^3y^2)^4)/((4x^7y^4)^2) =(3)/(x^2)`