Compare $25^{16}$ and $5^{30}$.

Compare $25^{16}$ and $5^{30}$.
  1. $25^{16} > 5^{30}$
  2. $25^{16} < 5^{30}$
  3. Equal
  4. None of these

Solution

$25^{16} = (5^{2})^{16} = 5^{32}$. Since $32 > 30$, $25^{16} > 5^{30}$.

Asked in: IMO

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