Question

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

Answer 1

`(−2x^4y^2z)(2x^2yz^2)^2=-8x^8y^4z^5`

Explanation:

First square everything in the right-hand bracket. `2^2 = 4`, and the index rules tell us we multiply the indices of each pronumeral (including the invisible 1 on the `y`) by 2:

`(−2x^4y^2z)(2x^2yz^2)^2=(−2x^4y^2z)(4x^4y^2z^4)`

Now we can multiply through the like terms. When we multiply we add indices. To simplify I've broken down that process:

`-2xx4=-8`
`x^4xxx^4=x^8`
`y^2xxy^2=y^4`
`zxxz^4=z^5`

Pulling all this together, we end up with:

`-8x^8y^4z^5`