irrational powers in Wolfram Alpha

Hi!
In this recent youtube video there is an interesting discussion about irrational powers:
https://www.youtube.com/watch?v=aYuzwNa0_4o
One of the claims in the video is that
1^p = e^(i*2*pi*k*p) for integers k
and that this will also hold in case p is an irrational number.
Wolfram Alpha will agree that the statement holds if we pick k = 1 and a rational number like 3/7:
https://www.wolframalpha.com/input?i=1%5E%283%2F7%29+%3D+e%5E%28i+2pi+%283%2F7%29%29+
But if you try to do it with an irrational number like sqrt(2), Wolfram Alpha says it's False (again with k=1).
https://www.wolframalpha.com/input?i=1%5E%28sqrt%282%29%29+%3D+e%5E%28i+2pi+%28sqrt%282%29%29%29+
Is there any alternative way to verify the statement with Wolfram Alpha for irrational numbers p?