a)Tính nhanh: $\frac{1978.1979+1980.21+1958}{1980.1979-1978.1979}$ b)Rút gọn: $\frac{5^{2}. 6^{11} . 16^{2} + 6^{2} . 12^{6} . 15^{2} }{2.6^{12}.10^{4}-81^{2}.960^{3}}$

`a)` `(1978.1979+1980.21+1958) / (1980.1979-1978.1979)`

`= (1978.1979 + (1979+1).21 + 1958) / (1979.(1980-1978))`

`= (1978.1979 + 1979.21 + 21 + 1958) / (1979.2)`

`= (1978.1979 + 1979.21 + 1979) / (1979.2)`

`= (1979.(1978 + 21 + 1)) / (1979.2)`

`= (1979.2000) / (1979.2)`

`= 2000/2`

`= 1000`

`b)` `(5^2.6^11.16^2+6^2.12^6.15^2) / (2.6^12.10^4-81^2.960^3)`

Tử số: `5^2.6^11.16^2+6^2.12^6.15^2`

`= 5^2.(2.3)^11.(2^4)^2 + (2.3)^2.(2^2.3)^6.(3.5)^2`

`= 5^2.2^11.3^11.2^8 + 2^2.3^2.2^12.3^6.3^2.5^2`

`= 2^19.3^11.5^2 + 2^14.3^10.5^2`

`= 2^14.3^10.5^2(2^5.3 + 1)`

`= 2^14.3^10.5^2 . 97`

Mẫu số: `2.6^12.10^4-81^2.960^3`

`= 2.(2.3)^12.(2.5)^4 - (3^4)^2.(2^6.3.5)^3`

`= 2 . 2^12 . 3^12 .2^4 .5^4 - 3^8 .2^18 .3^3 .5^3`

`= 2^17 . 3^12.5^4 - 2^18 .3^11 .5^3`

`= 2^17 . 3^11 . 5^3(3.5 - 2)`

`= 2^17.3^11.5^3 . 13` 

Suy ra:

`(2^14.3^10.5^2 . 97) / (2^17.3^11.5^3 . 13)`

`= 97 / (2^3 . 3 . 5 . 13)` `= 97 / (8 . 3 . 5 . 13)`

`= 97 / 1560`