\[\begin{array}{l}
1)\,\,\,{2^{27}} = {2^{3.9}} = {\left( {{2^3}} \right)^9} = {8^9}.\\
{3^{18}} = {3^{2.9}} = {\left( {{3^2}} \right)^9} = {9^9}.\\
2)\,\,\,So\,\,sanh\,\,\,{10^{20\,}}\,\,\,va\,\,\,{90^{10}}\\
{10^{20}} = {\left( {{{10}^2}} \right)^{10}} = {100^{10}}\\
Vi\,\,100 > 90 \Rightarrow {100^{10}} > {90^{10}}\\
\Rightarrow {10^{20}} > {90^{10}}\\
3)\,\,\,{27^n}:{3^n} = 9\\
\Leftrightarrow {\left( {\frac{{27}}{3}} \right)^n} = 9\\
\Leftrightarrow {9^n} = 9\\
\Leftrightarrow n = 1.
\end{array}\]
