# A special exponent

**Algebra**Level 3

\[\large \begin {cases} x = a^b = b^a\\ b = a^a\\ a \neq b\end {cases} \]

The above system of equations is true for only one triplet of positive integers \((x, a, b)\). What is \(x\)?

\[\large \begin {cases} x = a^b = b^a\\ b = a^a\\ a \neq b\end {cases} \]

The above system of equations is true for only one triplet of positive integers \((x, a, b)\). What is \(x\)?

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