Rút gọn:

\[\frac{{{6^8} \cdot {2^4} - {4^5} \cdot {{18}^4}}}{{{{27}^3} \cdot {8^4} - {3^9} \cdot {2^{13}}}}\]

Lời giải:

\[\frac{{{6^8} \cdot {2^4} - {4^5} \cdot {{18}^4}}}{{{{27}^3} \cdot {8^4} - {3^9} \cdot {2^{13}}}}\]

\[ = \frac{{{2^8} \cdot {3^8} \cdot {2^4} - {2^{2 \cdot 5}} \cdot {3^{2 \cdot 4}} \cdot {2^4}}}{{{3^{3 \cdot 3}} \cdot {2^{3 \cdot 4}} - {3^9} \cdot {2^{13}}}}\]

\[ = \frac{{{2^{12}} \cdot {3^8} - {2^{14}} \cdot {3^8}}}{{{3^9} \cdot {2^{12}} - {3^9} \cdot {2^{13}}}}\]

\[ = \frac{{{2^{12}} \cdot {3^8}\left( {1 - {2^2}} \right)}}{{{3^9} \cdot {2^{12}} \cdot \left( {1 - 2} \right)}}\]

\[ = \frac{{{3^8} \cdot \left( { - 3} \right)}}{{3 \cdot \left( { - 1} \right)}} = {3^8}.\]