2009 AIME II Problem 2

Suppose that a, b, and c are positive real numbers 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}.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.