Question

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

Answer 1

See the entire simplification process below:

Explanation:

First, use these rules of exponents to simplify the exponent outside the parenthesis:

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

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

`x^6y^0z^-3`

We can now use this rule of exponents to eliminate the `y` term:

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

`x^6y^color(red)(0)z^-3 = x^6 xx 1 xx z^-3 = x^6z^-3`

If we want to eliminate all negative exponents we can now use this rule of exponents:

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

`x^6z^color(red)(-3) = x^6/z^color(red)(- -3) = x^6/z^3`