Đáp án+Giải thích các bước giải:
$\displaystyle \begin{array}{{>{\displaystyle}l}} b) \ \frac{8^{2} .8^{3}}{2^{8} .2^{7}} =\frac{8^{5}}{2^{15}} =\frac{\left( 2^{3}\right)^{5}}{2^{15}} =\frac{2^{15}}{2^{15}} =1\\ b) \ \frac{2^{5} .6^{3}}{8^{3} .9^{2}} =\ \frac{2^{5} .( 2.3)^{3}}{\left( 2^{3}\right)^{3}\left( 3^{2}\right)^{2}} =\frac{2^{8} .3^{3}}{2^{9} .3^{4}} =\frac{1}{2.3} =\frac{1}{6}\\ c) \ \frac{9^{8} .8^{6}}{16^{4} .3^{17}} =\frac{\left( 3^{2}\right)^{8} .\left( 2^{3}\right)^{6}}{\left( 2^{4}\right)^{4} .3^{17}} =\frac{3^{16} .2^{18}}{2^{16} .3^{17}} =\frac{2^{2}}{3} =\frac{4}{3}\\ d)\frac{16^{11} .( -5)^{40}}{( -10)^{41}} =\frac{\left( 2^{4}\right)^{11} .( -5)^{40}}{( -5.2)^{41}} =\frac{2^{44} .( -5)^{40}}{( -5)^{41} .2^{41}} =\frac{2^{3}}{-5} =\frac{-8}{5}\\ e) \ \frac{4^{5} .9^{4} -2.6^{9}}{2^{10} .3^{8} +6^{8} .20} =\frac{\left( 2^{2}\right)^{5}\left( 3^{2}\right)^{4} -2.( 2.3)^{9}}{2^{10} .3^{8} +( 2.3)^{8} .\left( 2^{2} .5\right)} =\frac{2^{10} .3^{8} -2^{10} .3^{9}}{2^{10} .3^{8} -2^{10} .3^{8} .5} =\frac{2^{10} .3^{8}( 1-3)}{2^{10} .3^{8}( 1+5)} =\frac{-1}{3}\\ f) \ \frac{2^{10} .3^{31} -2^{40} .3^{6}}{2^{11} .3^{31} -2^{41} .3^{6}} =\frac{2^{10} .3^{6}\left( 3^{25} -2^{30}\right)}{2^{11} .3^{6}\left( 3^{25} -2^{30}\right)} =\frac{1}{2} \end{array}$
