Question

Which of the following is equivalent to [ (x^ 2 y^ 3 )^ -2/ (x^ 6 y^ 3 z)^3]? worth 60 points!

Answer 1

`\displaystyle (1)/(x^(48)y^(36)z^6)`

Explanation:

`\displaystyle[((x^2 y^3)^(-2))/((x^6 y^3 z)^2 ) ]^3`

`\displaystyle ((x^2 y^3)^(-6))/((x^6 y^3 z)^6 )`

`\displaystyle ((x^(-12) y^(-18)))/((x^(36) y^(18)z^6 ) )`

`\displaystyle (x^(-48) y^(-36))/(z^6 )`

`\displaystyle (1)/(x^(48)y^(36)z^6)`

Answer 2

`(1)/(x^(48)y^(36)z^(6))`

Explanation:

`(((x^2y^3)^(-2))/((x^6y^3z)^(2)))^3 =`

`= ((1)/((x^6y^3z)^(2)(x^2y^3)^(2)))^3`

`= ((1)/(x^(12)y^6z^(2)x^4y^6))^3`

`= ((1)/(x^(16)y^(12)z^(2)))^3`

`= (1)/(x^(48)y^(36)z^(6))`