Question

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

Answer 1

`1/(16x^12y^8z^12)`

Explanation:

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

First, to make the exponent outside of the parenthesis positive, we have to flip the the stuff inside to be the denominator, like this:
`(1/(2x^3y^2z^3))^4`

Now, we have to power everything to the fourth.
`1^4 = 1`
`2^4 = 16`
`(x^3)^4 = x^12` (when you have an exponent to an exponent you multiply them)
`(y^2)^4 = y^8`
`(z^3)^4 = z^12`

So when you put them together it becomes:
`1/(16x^12y^8z^12)`