Bài 1: (2,0 điểm) Tính hợp lí (nếu có thể): a) $\frac{-15}{14}$ : $\frac{17}{23}$ - $\frac{15}{14}$ : $\frac{17}{11}$ - $\frac{6}{7}$ b) ($\frac{-5}{3}$ + $\frac{-3}{2}$) : $\frac{17}{13}$ + ($\frac{7}{2}$ + $\frac{-1}{3}$) : $\frac{17}{13}$ c) 3².$\frac{1}{243}$.81².$\frac{1}{3³}$ d) (4.$2^{5}$) : ($2^{3}$.$\frac{1}{16}$)

Bài `1:`

`a)` `(-15)/14 : 17/23 - 15/14 : 17/11 - 6/7`

`=` `15/14 : (-17)/23 - 15/14 . 11/17 - 6/7`

`= 15/14 . (-23)/17 - 15/14 . 11/17 - 6/7`

`= 15/14 . ((-23)/17 - 11/17) - 6/7`

`= 15/14 . (-2) - 6/7`

`= (-30)/14 - 6/7`

`= (-3)`

`b)` `((-5)/3 + (-3)/2) : 17/13 + (7/2 + (-1)/3) : 17/13`

`= ((-5)/3 + (-3)/2) . 13/17 + (7/2 + (-1)/3) . 13/17`

`= ((-5)/3 + (-3)/2 + 7/2 + (-1)/3) . 13/17`

`= [ ((-5)/3 + (-1)/3) + ((-3)/2 + 7/2)] . 13/17`

`= [-2 + 2] . 13/17`

`= 0 . 13/17`

`= 0`

`c)` `3^2 . 1/243 . 81^2 . 1/3^3`

`= (3^2 . 3^8)/(3^5 . 3^3)`

`=(3^(2+8))/(3^(5+3))`

`= (3^10)/(3^8)`

`= 3^2`

`= 9`

`d)` `(4 . 2^5) : (2^3 . 1/16)`

`= (2^2 . 2^5) : (8 . 1/16)`

`=(2^(2+5)) : 8/16`

`= 2^7 : 1/2`

`= 2^7 . 2`

`=2^(7+1)`

`= 2^8`