What is the value of

$2^{-100}\cdot2^{-99}\cdot2^{-98}\cdots2^{-1}\cdot2^{0}\cdot2^{1}\cdots 2^{98}\cdot2^{99}\cdot2^{100} = \quad?$

$1$
$2$
$0$
$2^{100}$

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$\begin{aligned} \text{Expression } &= 2^{-100}\cdot2^{-99}\cdot2^{-98}\cdots2^{-1}\cdot2^{0}\cdot2^{1}\cdots2^{98}\cdot2^{99}\cdot2^{100} \\ &= \cancel{\frac{1}{2^{100}}\cdot\frac{1}{2^{99}} \cdot \frac{1}{2^{98}} \cdots \frac{1}{2^{1}}}\cdot 2^{0} \cdot \cancel{2^{1}\cdots2^{98}\cdot2^{99}\cdot2^{100}} \\ &= 2^0 \\ &= \boxed{1} \end{aligned}$