Question

Which expression is equivalent to the answer and show work pls I am force to write it down :,)

Answer 1

Last option:

`(4x^4y^2)/(z)`

Explanation:

Original expression is

`(12x^6y^(-4)z^2)/(3x^2y^(-6)z^3)\\\\`

Let us eliminate the obvious wrong answers

`(12)/(3) = 4\\\\`

so the coefficient in the answer should be 4.

We can eliminate first and third choices

Now for each term with the same variable, compute the division

`(x^6)/(x^2) = x^(6-2) = x^4\\\\`

Second choice is out so the last choice is the correct one.

We can go further with the other terms

`(y^(-4))/(y^(-6)) = y^(-4 - (-6)) = y ^(-4+6) = y^2`

`(z^2)/(z^3) = z^(2-3) = z^(-1) = (1)/(z)`

Multiplying all these individual terms gives

`4 \cdot x^4 \cdot y^2 \cdot (1)/(z)\\\\= (4x^4y^2)/(z)`