`1)(4^{2}.4^3)/2^10=(4^5)/2^10=2^10/2^10=1`

`2)(2^{7}.9^3)/(6^{5}.8^2)`

`=(2^{7}.3^6)/(2^{5}.3^{5}.2^6)`

`=(2^{7}.3^6)/(2^{11}.3^5)`

`=3/2^4=3/16`

`3)(5^{4}.20^4)/(25^{5}.4^5)`

`=(20.5)^4/(25.4)^5`

`=100^4/100^5=1/100`

`x^3-7x-6=0`

`<=>x^3-x-6x-6=0`

`<=>x(x-1)(x+1)-6(x+1)=0`

`<=>(x+1)(x^2-x-6)=0`

`<=>(x+1)(x^2+2x-3x-6)=0`

`<=>(x+1)(x+2)(x-3)=0`

`<=>[(x=-1),(x=-2),(x=3):}`

`x^3-4x^2=-4x`

`<=>x(x^2-4x+4)=0`

`<=>x(x-2)^2=0`

`<=>[(x=0),(x=2):}`

`(2x+1)^2=(3+x)^2`

`<=>[(2x+1=x+3),(2x+1=-x+3):}`

`<=>[(x=2),(x=2/3):}`

`x^2+y^2-6x+6y+18=0`

`<=>x^2-6x+9+y^2+6y+9=0`

`<=>(x-3)^2+(y+3)^2=0`

`<=>{(x=3),(y=-3):}`

-64 nhe

`a)(x+8)(x-8)`

`=x^2-8^2=x^2-36`

`b)x^3+12x^2+48x+64`

`=x^3+3.x^{2}.4+3.x.4^2+4^3`

`=(x+4)^3`

`c)16x^2-8x+1`

`=(4x)^2-2.4x+1`

`=(4x-1)^2`

`d)9x^2+6x+1`

`=(3x)^2+2.3x+1`

`=(3x+1)^2`

`e)(x+2)(x^2-2x+4)`

`=(x+2)(x^2-x.2+2^2)`

`=x^3+2^3`

`=x^3+8`

`f)x^3+125`

`=x^3+5^3`

`=(x+5)(x^2-5x+125)`

-Anh em như thể tay chân

Rách lành đùm bọc dở hay đỡ đần

-Con có cha như nhà có nóc

`B=sqrt2.sqrt{2+sqrt3}-2/(sqrt3+1)`

`B=sqrt{2(2+sqrt3)}-(2(sqrt3-1))/((sqrt3-1)(sqrt3+1))`

`B=sqrt{4+2sqrt3}-(2(sqrt3-1))/(3-1)`

`B=sqrt{3+2sqrt3+1}-(2(sqrt3-1))/2`

`B=sqrt{(sqrt3+1)^2}-(sqrt3-1)`

`B=sqrt3+1-(sqrt3-1)=2`

`(-2/3x-3/5).(3/(-2)-10/3)=2/5`

`<=>(-2/3x-3/5).(-29/6)=2/5`

`<=>-2/3x-3/5=2/5:(-29/6)=-12/145`

`<=>-2/3x=15/29`

`<=>x=15/29:(-2/3)`

`<=>x=-45/58`

Vậy `x=-45/58`

`9B=(10^2025-1)=>B=(10^2025-1)/9`

`a)A=1+3+3^2+3^3+...+3^2012`

`=>3A=3+3^2+3^3+...+3^2013`

`=>3A-A=2A=3^2013-1`

`=>A=(3^2013-1)/2`

`b)B=1+10+10^2+...+10^2024`

`=>10B=10+10^2+10^3+....+10^2025`

`=>10B-B=9B=10^2025-10`

`=>B=(10^2025-10)/9`