`4)`

`a)`

`x^3 (-5/4 x^2 y)(2/5 x^3 y^4)`

`=(-5/4 x^5 y)(2/5 x^3 y^4)`

`=-1/2 x^8 y^5`

`b)`

`(-3/4 x^5 y^4)(xy^2)(-8/9 x^2 y^5)`

`=(-3/4 x^6 y^6)(-8/9 x^2 y^5)`

`=2/3 x^8 y^11`.

`5)`

`a)`

`(x^2 y+xy^2 -3xyz)+(2x^2 y+3xy^2 +3xyz+2)`

`=(x^2 y+2x^2 y)+(xy^2 +3xy^2) + (-3xyz+3xyz)+2`

`=3x^2 y+4xy^2 +2`

`b)`

`(\sqrt{3}xy^3 - 7x^3 y+51x^2 y^2 -27) -(\sqrt{3}xy^3 +51x^2 y^2 +23)`

`=(\sqrt{3}xy^3 - \sqrt{3}xy^3) +(-7x^3 y)+(51x^2 y^2 - 51x^2 y^2) + (-27-23)`

`=-7x^3 y-50`.