Question

What is the result when the monomial `-5x^3y^2z` is raised to the third power?

Answer 1

See a solution process below:

Explanation:

First, we can write the given monomial raised to the third power as:

`(-5x^3y^2z)^3`

Now, we can use these rules of exponents to simplify this expression:

`a = a^color(red)(1)` and `(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))`

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

`-5^(color(red)(1) xx color(blue)(3))x^(color(red)(3) xx color(blue)(3))y^(color(red)(2) xx color(blue)(3))z^(color(red)(1) xx color(blue)(3)) =>`

`-5^3x^9y^6z^3 =>`

`-125x^9y^6z^3 =>`