Bài 1 : Rút gọn các biểu thức sau : a, A = 15 . 4^12.9^7-4.3^15.8^8 / 19 . 2^24 . 3^14-6.4^12.27^5 b, B = 2^18 . 18^7.3^3 + 3^15.2^15 / 2^10 . 6^15 + 3^14 .15.4^13 Cứu mình với

Đáp án+Giải thích các bước giải:

 `a)`

`A=\frac{15.4^{12}.9^{7}-4.3^{15}.8^{8}}{19.2^{24}.3^{14}-6.4^{12}.27^{5}}`

`=\frac{3.5.(2^{2})^{12}.(3^{2})^{7}-2^{2}.3^{15}.(2^{3})^{8}}{19.2^{24}.3^{14}-2.3.(2^{2})^{12}.(3^{3})^{5}}`

`=\frac{3.5.2^{24}.3^{14}-2^{2}.3^{15}.2^{24}}{19.2^{24}.3^{14}-2.3.2^{24}.3^{15}}`

`=\frac{2^{24}.3^{14}.(3.5-4.3)}{2^{24}.19.3^{14}-6.2^{24}.3^{15}}`

`=\frac{3^{15}.2^{24}.(15-12)}{2^{24}.3^{14}.(19-6.3)}`

`=3/1`

`=3`

Vậy `A=3`

`b)`

`B=\frac{2^{18}.18^{7}.3^{3}+3^{15}.2^{15}}{2^{10}.6^{15}+3^{14}.15.4^{13}}`

`=\frac{2^{18}.(2.3^{2})^{7}.3^{3}+3^{15}.2^{15}}{2^{10}.(2.3)^{15}+3^{14}.3.5.(2^{2})^{13}}`

`=\frac{2^{18}.2^{7}.3^{14}.3^{3}+3^{15}.2^{15}}{2^{10}.2^{15}.3^{15}+3^{15}.5.2^{26}}`

`=\frac{2^{25}.3^{17}+3^{15}.2^{15}}{2^{25}.3^{15}+3^{14}.3.5.2^{26}}`

`=\frac{2^{15}.3^{15}.(2^{10}.3^{2}+1)}{2^{15}.3^{14}.(2^{10}.3+15.2^{11})}`

`=\frac{3.(9216+1)}{3072+15.2048}`

`=\frac{3.9217}{33792}`

`=\frac{9217}{11264}`

Vậy `B=\frac{9217}{11264}`