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# An interesting inequality

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

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

Note by Indulal Gopal
1 year ago

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Raise 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. · 1 year ago