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Algebra Level 3

If \( a = \log_x y^\pi + \log_y x^e \) and \( b = \dfrac1{\log_y x^{1/\pi} } - \dfrac1{\log_x y^{1/e}} \), compute \( \dfrac{x^{a+b+2e}}{y^{a-b+2\pi}} \).


This question was taken from IME (Instituto Militar de Engenharia - Brazil)
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