Question

How do you divide `\frac { 2x ^ { 4} y ^ { - 4} z ^ { - 3} } { 3x ^ { 2} y ^ { - y } z ^ { 4} }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression to make it easier to manipulate:

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

Next, use this rule of exponents to divide the `x` and `y` terms:

`x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))`

`2/3(x^color(red)(4)/x^color(blue)(2))(y^color(red)(-4)/y^color(blue)(-y))(z^-3/z^4) =>`

`2/3x^(color(red)(4)-color(blue)(2))y^(color(red)(-4)-color(blue)(-y))(z^-3/z^4) =>`

`2/3x^(color(red)(4)-color(blue)(2))y^(color(red)(-4)+color(blue)(y))(z^-3/z^4) =>`

`2/3x^2y^(-4+y)(z^-3/z^4) =>`

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

Now, use this rule of exponents to divide the `z` term:

`x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))`

`2/3x^2y^(y-4)(z^color(red)(-3)/z^color(blue)(4)) =>`

`2/3x^2y^(y-4)1/z^(color(blue)(4)-color(red)(-3)) =>`

`2/3x^2y^(y-4)1/z^(color(blue)(4)+color(red)(3)) =>`

`2/3x^2y^(y-4)1/z^7 =>`

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