First-order logic : is this a correct way to say ' x is a power of 2 ' in first order number theory?

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0 < x ∧ ∀y ((1 < y ∧ ∃z x = y × z) → ∃z y = z + z).

I'm confused about the last part. ∃z y = z + z by itself would be fine, but haven't we already used z? I'm also not clear on free/ bounded variables, so that might also be it.

Also, what is the difference between ∀x∀y F and ∀x (∀y F)? What do the brackets indicate?

Lastly, our professor told us to always consider what variable the statement is about. In this case, it's about x, but we haven't quantified x anywhere..