`(2012xx2013+2014)/(2012xx2014+2)`

`=(2012xx(2014-1)+2014)/(2012xx2014+2)`

`=(2012xx2014-2012+2014)/(2012xx2014+2)`

`=(2012xx2014+2)/(2012xx2014+2)`

`=1`

`(a):`

`10^{3}xx10^{5}xx100`

`=10^{3}xx10^{5}xx10^{2}`

`=10^{3+5+2}`

`=10^{10}`

`(b):`

`15^{3}xx625`

`=(5xx3)^{3}xx(5xx5)^{2}`

`=5^{3}xx3^{3}xx5^{2}xx5^{2}`

`=5^{3+2+2}xx3^{3}`

`=5^{7}xx3^{3}`

`(2x+3)(3-2x)+(2x-1)^{2}=2`

`<=>3^{2}-(2x)^{2}+(2x)^{2}-2.2x.1+1^{2}=2`

`<=>9-4x^{2}+4x^{2}-4x+1=2`

`<=>-4x+10=2`

`<=>-4x=-8`

`<=>x=2`

`(1)/(2)+(5)/(6)xx(12)/(15)`

`=(1)/(2)+(5xx6xx2)/(6xx5xx3)`

`=(1)/(2)+(2)/(3)`

`=(3)/(6)+(4)/(6)`

`=(7)/(6)`

`(2x-1)^{2}+(x+3)^{2}-5(x+7)(x-7)=0`

`<=>4x^{2}-4x+1+x^{2}+6x+9-5(x^{2}-49)=0`

`<=>5x^{2}+2x+10-5x^{2}+245=0`

`<=>2x+255=0`

`<=>2x=-255`

`<=>x=-255/2`

`45x(y-8)+27x(8-y)`

`=45x(y-8)-27x(y-8)`

`=(45x-27x).(y-8)`

`=18x(y-8)`

`(e):\  25(2x-y-3z)^{14}:5(y+3z-2x)^{7}`

`=25(y+3z-2x)^{14}:5(y+3z-2x)^{7}`

`=5(y+3z-2x)^{14-7}`

`=5(y+3z-2x)^{7}`

`(g):\   (8x^{3}+36x^{2}+54x+27):(3+2x)^{2}`

`=(2x+3)^{3}:(2x+3)^{2}`

`=(2x+3)^{3-2}`

`=2x+3`

`(a):\  x^{7}.(3y^{2}z^{3})^{3}:9(x^{2}y^{3}z^{3})^{2}`

`=27x^{7}y^{6}z^{9}:9x^{4}y^{6}z^{6}`

`=3x^{3}z^{3}`

`(c)\  24(x-2y)^{4}:12(2y-x)^{3}`

`=24(2y-x)^{4}:12(2y-x)^{3}`

`=2(2y-x)`

`=4y-2x`

+) `9^{9}:27^{3}`

`=(3^{2})^{9}:(3^{3})^{3}`

`=3^{2.9}:3^{3.3}`

`=3^{18}:3^{9}`

`=3^{18-9}=3^{9}`

``

+) `3^{2}.3^{5}=3^{2+5}=3^{7}`

Vì : `3^{9}>3^{7}`

`=>9^{9}:27^{3}>3^{2}.3^{5}`

`4/5+3/7`

`=(4xx7)/(5xx7)+(3xx5)/(7xx5)`

`=(28)/(35)+(15)/(35)`

`=(28+15)/(35)`

`=(43)/(35)`