Question

How do you evaluate `(- 3x ^ { 3} y ^ { 4} z ^ { 2} ) ( x y z ^ { 2} ) ( - x ^ { 5} y ^ { 2} z )`?

Answer 1

See a solution process below:

Explanation:

First, rearrange the expression as:

`(-3x^3y^4z^2)(xyz^2)(-x^5y^2z) =>`

`(-3x^3y^4z^2)(xyz^2)(-1x^5y^2z) =>`

`(-3 * -1)(x^3 * x * x^5)(y^4 * y * y^2)(z^2 * z^2 * z) =>`

`3(x^3 * x * x^5)(y^4 * y * y^2)(z^2 * z^2 * z)`

Next, use this rule for exponents to rewrite the expression:

`a = a^color(red)(1)`

`3(x^3 * x^color(red)(1) * x^5)(y^4 * y^color(red)(1) * y^2)(z^2 * z^2 * z^color(red)(1))`

Now, use this rule of exponents to complete the evaluation:

`x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))`

`3(x^color(blue)(3) * x^color(red)(1) * x^color(green)(5))(y^color(blue)(4) * y^color(red)(1) * y^color(green)(2))(z^color(blue)(2) * z^color(green)(2) * z^color(red)(1)) =>`

`3x^(color(blue)(3)+color(red)(1)+color(green)(5))y^(color(blue)(4)+color(red)(1)+color(green)(2))z^(color(blue)(2)+color(green)(2)+color(red)(1)) =>`

`3x^9y^7z^5`

Answer 2

`3x^9y^7z^5`

Explanation:

Take each different term and multiply them. Powers multiply by adding the exponents.
`-3*-1=3`
`x^3*x^1*x^5=x^9`
`y^4*y^1*y^2=y^7`
`z^2*z^2*z^1=z^5`