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Suppose that \(a, b, c \in \mathbb {R^{+}}\) , such that \(a^{\log_3 7} = 27\) , \(b^{\log_7 11} = 49\) , and \(c^{\log_{11}25} = \sqrt{11}\) . Find \[a^{(\log_3 7)^2} + b^{(\log_7 11)^2} + c^{(\log_{11} 25)^2}.\]

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