Đáp án:
$\begin{array}{l}
\dfrac{{{3^6}{{.21}^{12}}}}{{{{175}^9}{{.7}^3}}} = \dfrac{{{3^6}.{{\left( {3.7} \right)}^{12}}}}{{{{\left( {{{7.5}^2}} \right)}^9}{{.7}^3}}} = \dfrac{{{3^6}{{.3}^{12}}{{.7}^{12}}}}{{{7^9}{{.5}^{18}}{{.7}^3}}} = \dfrac{{{3^{18}}}}{{{5^{18}}}} = {\left( {\dfrac{3}{5}} \right)^{18}}\\
\dfrac{{{3^{10}}{{.6}^7}.4}}{{{{10}^9}{{.5}^8}}} = \dfrac{{{3^{10}}{{.3}^7}{{.2}^7}{{.2}^2}}}{{{2^9}{{.5}^9}{{.5}^8}}} = \dfrac{{{3^{17}}{{.2}^9}}}{{{2^9}{{.5}^{17}}}} = \dfrac{{{3^{17}}}}{{{5^{17}}}} = {\left( {\dfrac{3}{5}} \right)^{17}}\\
Do:0 < \dfrac{3}{5} < 1\\
\Leftrightarrow {\left( {\dfrac{3}{5}} \right)^{18}} < {\left( {\dfrac{3}{5}} \right)^{17}}\\
\Leftrightarrow \dfrac{{{3^6}{{.21}^{12}}}}{{{{175}^9}{{.7}^3}}} < \dfrac{{{3^{10}}{{.6}^7}.4}}{{{{10}^9}{{.5}^8}}}
\end{array}$
