Prove that for any positive integer values of \(m\) and \(n\), the following inequalities are fulfilled.

\[ \large 2^{mn} > m^n, \quad 2^{mn} > n^m \]

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## Comments

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TopNewestRaise both sides of the first inequality by \(\frac 1 n\) and both sides of the second inequality by \(\frac 1 m\).

You get \(2^m>m\) in the first inequality and \(2^n>n\) in the second inequality which are both true.

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