Is it true that $z^{w+1}=z^w\cdot z$ where $z,w\in \Bbb{C}$? The original question didn't state whether $w\in \Bbb{C}$, but I guess that would be the case, and it is a more inclusive approach. I arrived at $e^{(w+1)\log(z)}=e^{w\log(z)}\cdot e^{\log(z)}$, and it seems just about it. I don't even refer to the existence of the branches above, and it doesn't seem like I need to. I just don't see the point in requiring such a short process. Could you contribute your perspective?
2026-03-25 05:07:40.1774415260
Is it true that $z^{w+1}=z^w\cdot z$ where $z,w\in \Bbb{C}$?
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