Giải thích các bước giải:
Ta có:
\[\begin{array}{l}
\frac{{{4^{15}}}}{{{7^{30}}}} = \frac{{{{\left( {{2^2}} \right)}^{15}}}}{{{7^{30}}}} = \frac{{{2^{30}}}}{{{7^{30}}}} = {\left( {\frac{2}{7}} \right)^{30}}\\
\frac{{{8^{10}}{{.3}^{30}}}}{{{7^{30}}{{.4}^{15}}}} = \frac{{{{\left( {{2^3}} \right)}^{10}}{{.3}^{30}}}}{{{7^{30}}.{{\left( {{2^2}} \right)}^{15}}}} = \frac{{{2^{30}}{{.3}^{30}}}}{{{7^{30}}{{.2}^{30}}}} = \frac{{{3^{30}}}}{{{7^{30}}}} = {\left( {\frac{3}{7}} \right)^{30}}\\
\frac{3}{7} > \frac{2}{7} \Rightarrow {\left( {\frac{3}{7}} \right)^{30}} > {\left( {\frac{2}{7}} \right)^{30}} \Leftrightarrow \frac{{{4^{15}}}}{{{7^{30}}}} < \frac{{{8^{10}}{{.3}^{30}}}}{{{7^{30}}{{.4}^{15}}}}
\end{array}\]
