`a)10x^2y^3:(-5xy^2)`

`=(10:-5)(x^2:x)(y^3:y^2)`

`=-2x^(2-1)y^(3-2)`

`=-2xy`

`b)4x^3y^6:10x^2y^2`

`=(4:10)(x^3:x^2)(y^6:y^2)`

`=2/5x^(3-2)y^(6-2)`

`=2/5xy^4`

`c)(x^4+12x^2-5x):(-x)`

`=x^4:(-x)+12x^2:(-x)-5x:(-x)`

`=-x^(4-1)-12x^(2-1)+5x^(1-1)`

`=-x^3-12x+5`

`d)(15x^5y^3-10x^3y^5+25x^4y^4):5x^2y^2`

`=15x^5y^3:5x^2y^2-10x^3y^5:5x^2y^2+25x^4y^4:5x^2y^2`

`=(15:5)(x^5:x^2)(y^3:y^2)-(10:5)(x^3:x^2)(y^5:y^2)+(25:5)(x^4:x^2)(y^4:y^2)`

`=3x^3y-2xy^3+5x^2y^2`