Đáp án:
$\begin{array}{l}
a)\dfrac{{{2^{32}}}}{{{2^n}}} > 16\\
\Leftrightarrow {2^{32 - n}} > {2^4}\\
\Leftrightarrow 32 - n > 4\\
\Leftrightarrow n < 28\\
\Leftrightarrow n \in \left\{ {0;1;2;3;...;26;27} \right\}\\
b)25 < {5^n} < 625\\
\Leftrightarrow {5^2} < {5^n} < {5^4}\\
\Leftrightarrow 2 < n < 4\\
\Leftrightarrow n = 3\\
Vậy\,n = 3\\
2)a){7^6} + {7^5} - {7^4}\\
= {7^4}\left( {{7^2} + 7 - 1} \right)\\
= {7^4}.55\\
= {7^4}.5.11 \vdots 11\\
b){10^9} + {10^8} + {10^7}\\
= {10^7}\left( {{{10}^2} + 10 + 1} \right)\\
= {10^7}.111\\
= {10^7}.3.37
\end{array}$
Không chia hết cho 22