Đáp án:
\[\frac{1}{2}\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\frac{{{2^{19}}{{.27}^3} - 15.{{\left( { - 4} \right)}^9}{{.9}^4}}}{{{6^9}{{.2}^{10}} + {{\left( { - 12} \right)}^{10}}}}\\
= \frac{{{2^{19}}{{.27}^3} + {{15.4}^9}{{.9}^4}}}{{{6^9}{{.2}^{10}} + {{12}^{10}}}}\\
= \frac{{{2^{19}}.{{\left( {{3^3}} \right)}^3} + 5.3.{{\left( {{2^2}} \right)}^9}.{{\left( {{3^2}} \right)}^4}}}{{{{\left( {2.3} \right)}^9}{{.2}^{10}} + {{\left( {{{3.2}^2}} \right)}^{10}}}}\\
= \frac{{{2^{19}}{{.3}^9} + {{5.2}^{18}}{{.3}^9}}}{{{2^{19}}{{.3}^9} + {3^{10}}{{.2}^{20}}}}\\
= \frac{{{2^{18}}{{.3}^9}.\left( {2 + 5} \right)}}{{{2^{18}}{{.3}^9}\left( {2 + 3.4} \right)}}\\
= \frac{7}{{14}} = \frac{1}{2}
\end{array}\)
