Question

How do you simplify `(- 3x ^ { 2} y ^ { 0} z ) ^ { 4}`?

Answer 1

See the entire solution process below:

Explanation:

First, use this rule of exponents to simplify the `z` term within the parenthesis:

`a^color(red)(0) = 1`

`(-3x^2y^color(red)(0)z)^4 = (-3x^2 1z)^4 = (-3x^2z)^4`

Now, we can use these two rules of exponents to complete the simplification:

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

`(-3x^2z)^4 = (-3^color(red)(1)x^color(red)(2)z^color(red)(1))^color(blue)(4) = -3^(color(red)(1) xx color(blue)(4))x^(color(red)(2) xx color(blue)(4))z^(color(red)(1) xx color(blue)(4)) =`

`-3^4x^8z^4 = 81x^8z^4`