Question

How do you simplify `\root [ 4] { x ^ { 10} y ^ { 25} z ^ { 19} }`?

Answer 1

`x^2y^6z^4root(4)(x^2yz^3)`

Explanation:

You are looking for powers of 4 that you can 'take outside' the root

Note the following:
`x^10 = (x^4)^2x^2 ->(x^2)^4x^2`
`y^25=(y^4)^6y->(y^6)^4y`
`z^19=(z^4)^4 z^3`

Write as `root(4)((x^4)^2x^2color(white)(.)(y^6)^4ycolor(white)(.)(z^4)^4z^3)` giving:

`x^2y^6z^4root(4)(x^2yz^3)`