Cross your limits 3

Calculus Level 4

\[ \large \lim_{x\to\infty} \dfrac{e^x \left( \left(2^{x^n}\right)^{1/e^x} - \left(3^{x^n}\right)^{1/e^x} \right)}{x^n} \]

Evaluate the limit above for positive integer \(n\).

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