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Let \( \left\{a_{n}\right\} \) and \( \left\{b_{n}\right\} \) are two sequences given by \( a_{n}=(x)^{1 / 2^{n}}+(y)^{1 / 2^{n}} \) and \( b_{n}=(x)^{1 / 2^{n}}-(y)^{1 / 2^{n}} \) for all \( n \in N \). Then find \( a_{1} a_{2} a_{3} \ldots \ldots . a_{n} \).
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