Answer
a) $xyz[x(3y-2x)]i+y(3z-2y)j+z(3x-2z)k]$
b) $y^2z^3+x^3z^2+x^2y^3$
Work Step by Step
a) Consider $F=A i+B j+C k$
Then $curl F=\begin{vmatrix}i&j&k\\\dfrac{\partial}{\partial x}&\dfrac{\partial }{\partial y}&\dfrac{\partial }{\partial z}\\A&B&C\end{vmatrix}$
$curl F=[C_y-B_z]i+[A_z-C_z]j+[B_x-A_y]k$
$curl F=(3x^2y^2z-2x^3yz)i+(3xy^2z^2-2xy^3z)j+(3x^2yz^2-2xyz^3)k=xyz[x(3y-2x)]i+y(3z-2y)j+z(3x-2z)k]$
b) $div F=\dfrac{\partial A}{\partial x}+\dfrac{\partial B}{\partial y}+\dfrac{\partial C}{\partial z}$
$div F=\dfrac{\partial [xy^2z^3]}{\partial x}+\dfrac{\partial [x^3yz^2]}{\partial y}+\dfrac{\partial [x^2y^3z]}{\partial z}=y^2z^3+x^3z^2+x^2y^3$