If \( \log _{5} x=a \) and \( \log _{2} y=a \), find \( 100^{2 a-1} \) in terms of \( x \) and \...

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If \( \log _{5} x=a \) and \( \log _{2} y=a \), find \( 100^{2 a-1} \) in terms of \( x \) and \( y \).
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