AIME Logarithm problem!

Level 2

Suppose that $$a,b,c$$ are real positive integers such that,$a^{\log_{3}7}=27,b^{\log_{7}11}=49,c^{\log_{11}25}=\sqrt{11}$.Find the value of,$a^{(\log_{3}7)^{2}}+b^{(\log_{7}11)^2}+c^{(\log_{11}25)^2}$.

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