Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 5.0 AIME, harder Prove it Philippines

Problem:
Find all real values of $x$ that satisfy the equation $x^{x^{2010}} = x^{2010}$ .

Solution

Solution:
$\sqrt[2010]{2010}$

$-\sqrt[2010]{2010}, 1$

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