Question

How do you simplify `root5(-t^10 )`?

Answer 1

`root(5)(-t^10) = -t^2`

Explanation:

If `a > 0` and `b, c >= 0`, then `a^(bc) = (a^b)^c`

Also `root(n)(-a) = -root(n)(a)` if `n in ZZ` is odd.

So `root(5)(-t^10) = -root(5)(t^10) = -(t^10)^(1/5) = -t^(10*1/5) = -t^2`

We can also see that `(-t^2)^5 = (-1)^5*(t^2)^5 = -t^10`, so `-t^2` is a fifth root of `-t^10`.