`1)-3x^4yz(-1/6x^3yz^2)(-5/2x^4y^3z)`

`=(-3*-1/6*-5/2)(x^4*x^3*x^4)(y*y*y^3)(z*z^2*z)`

`=-5/4x^(4+3+4)y^(1+1+3)z^(1+2+1)`

`=-5/4x^11y^5z^4`

`2)-4(2x)^2y^3+1/2xy(-2xy^2)+1/4x^2y^3`

`=-4(4x^2)y^3-x^2y^3+1/4x^2y^3`

`=-16x^2y^3-x^2y^3+1/4x^2y^3`

`=x^2y^3(-16-1+1/4)`

`=-67/4x^2y^3`

`3)3/5x^4y^3z^5(-3/10xy^5z)(-2/7x^5yz)`

`=(3/5*-3/10*-2/7)(x^4*x*x^5)(y^3*y^5*y)(z^5*z*z)`

`=9/175x^(4+1+5)y^(3+5+1)z^(5+1+1)`

`=9/175x^10y^9z^7`

`4)1/3x^4y-5/3x^3(5/2xy)+3/4x^4y`

`=1/3x^4y-25/6x^4y+3/4x^4y`

`=x^4y(1/3-25/6+3/4)`

`=-37/12x^4y`