Inspired by Nihar Mahajan

Algebra Level 2

\[ \Large \color{red}{a}^{\color{green}{c}} > \color{blue}{b}^{\color{green}{c}} \]

Given that \(\color{red}{a},\) \(\color{blue}{b},\) and \(\color{green}{c} \) are real numbers such that

  • \(\color{red}{a} \color{blue}{b} > 0\).
  • \( \color{green}{c} > 0 \).
  • \( \color{green}{c} \) is not an even integer.
  • \( \color{red}{a} > \color{blue}{b} \).

What can be said about the very first statement above?


Inspiration.

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