Calculating $e^{j2\pi t}$ in two ways gives different results: $\cos(2\pi t)+j \sin(2\pi t)$ vs $1^t$

Question

I've encountered the following equations while studying complex exponentials: $$\begin{align} e^{j2\pi t} &= \cos(2\pi t) + j \sin(2\pi t) \tag1\\[4pt] e^{j2\pi t} &= (e^{j2\pi})^t = (\cos(2\pi) + j\sin(2\pi))^t = (1+0)^t = 1^t \tag2 \end{align}$$ Upon comparing (1) and (2), it's evident that they represent different expressions. However, theoretically, these equations should yield the same result.

Could someone help clarify this result?