Đáp án:
$\begin{array}{l}
a){3^4} < \dfrac{1}{9}{.27^n} < {3^{10}}\\
\Rightarrow {3^4} < \dfrac{1}{{{3^2}}}.{\left( {{3^3}} \right)^n} < {3^{10}}\\
\Rightarrow {3^4} < {3^{3n - 2}} < {3^{10}}\\
\Rightarrow 4 < 3n - 2 < 10\\
\Rightarrow 6 < 3n < 12\\
\Rightarrow 2 < n < 4\\
Do:n \in Z\\
\Rightarrow n = 3\\
Vậy\,n = 3\\
b)7;\left( { - 3} \right);6;\left( { - 14} \right)\\
Do:6.7 = 42 = \left( { - 3} \right).\left( { - 14} \right)\\
\Rightarrow 6.7 = \left( { - 3} \right).\left( { - 14} \right)\\
\Rightarrow \left\{ \begin{array}{l}
\dfrac{6}{{ - 3}} = \dfrac{{ - 14}}{7}\\
\dfrac{6}{{ - 14}} = \dfrac{{ - 3}}{7}\\
\dfrac{{ - 3}}{6} = \dfrac{7}{{ - 14}}\\
\dfrac{7}{{ - 3}} = \dfrac{{ - 14}}{6}
\end{array} \right.
\end{array}$
