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

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

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

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

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

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. – Brilliant Member · 1 year, 5 months ago

Log in to reply