Đáp án:
$\displaystyle \begin{array}{{>{\displaystyle}l}} A=\frac{1}{6}\\ B=\frac{5}{3} \end{array}$
Giải thích các bước giải:
$\displaystyle \begin{array}{{>{\displaystyle}l}} A=\frac{2^{12} .3^{5} -4^{6} .81}{\left( 2^{2} .3\right)^{6} +8^{4} .3^{5}} =\frac{2^{12} .3^{5} -2^{12} .3^{4}}{2^{12} .3^{6} +2^{12} .3^{5}}\\ =\frac{2^{12} .3^{4} .( 3-1)}{2^{12} .3^{4} .\left( 3^{2} +3\right)} =\frac{1}{6}\\ B=\frac{30.4^{7} .3^{29} -5.14^{5} .2^{12}}{54.6^{14} .9^{7} -12.8^{5} .7^{5}} =\frac{3^{30} .2^{15} .5-2^{17} .5.7^{5}}{3^{3} .2.2^{14} .3^{14} .3^{14} -2^{2} .3.2^{15} .7^{5}}\\ =\frac{2^{15} .\left( 3^{30} .5-2^{2} .5.7^{5}\right)}{2^{15} .\left( 3^{31} -2^{2} .3.7^{5}\right)} =\frac{5.\left( 3^{30} -2^{2} .7^{5}\right)}{3.\left( 3^{30} -2^{2} .7^{5}\right)} =\frac{5}{3} \end{array}$
