If $z=\frac{(\sqrt 3 - i)^{99}}{(1-i)^{101}}$, then the value of $\left(|z|\right)^{\frac{2}{97}}$

Question

Answer given below. This question has been posted for a friend. Since it’s only adding information to the site and nothing else, I don’t think it should be taken down just for being irrelevant.

Answer 1

$$|z|=\left[\frac{2^{99}}{\sqrt 2^{101}}\right]$$ $$=2^{\frac{97}{2}}$$ Then the value of expression asked is $$=\left(2^{\frac{97}{2}}\right)^{\frac{2}{97}}$$ $$=2$$