Toán Lớp 9: rút gọn biểu thức `A=(2^12 .3^5-4^6 .81)/((2^2. 3)^6+8^4. 3^5)` `B=(30. 4^7. 3^29-5.14^5. 2^12)/(54. 6^14. 9^7-12.8^5. 7^5)`

Question

Toán Lớp 9:  rút gọn biểu thức A=(2^12 .3^5-4^6 .81)/((2^2. 3)^6+8^4. 3^5) B=(30. 4^7. 3^29-5.14^5. 2^12)/(54. 6^14. 9^7-12.8^5. 7^5)

lanminhngoc · Answer

Giải đáp:    $ displaystyle  begin{array}{{>{ displaystyle}l}} A= frac{1}{6}   B= frac{5}{3}  end{array}$    Lời giải và giải thích chi tiết:    $ 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}$