Use `RandomRat` to test whether `((-1)^(1/Denominator[q]))^Numerator[q]` is identical with `(-1)^q`. Use `25000` rational numbers between `1` and `500000`. Use `Delta =10^-10` and `Map` it to a large list of random rational numbers. If you always get `True` you have evidence for the identity.

Then, show that 

```
((-1)^Numerator[q])^(1/Denominator[q])==(-1)^q

```

is not an identity. 

---

So far this is what I have:

```
RandomRat := ((-1)^(1/Denominator[q]))^(Numerator[q])
(-1)^q == RandomRat

```

I'm not sure if that's correct so far because I think I'd have to use pure functions and then how would I use the `25000` rational numbers between `1` and `500000` from here?