If area (A), velocity (v) and density (p) are taken as fundamental units, what is the dimensional formula for force?

Let ,$\mathrm{F}={{\mathrm{A}}^{\mathrm{x}}}_{\mathrm{v}}^{\mathrm{y}}{\mathrm{\rho }}^{\mathrm{z}}, \mathrm{then}$
$\left[{\text{MLT}}^{-2}\right]={\left[{\text{L}}^2\right]}^{\mathrm{x}}{\left[{\text{LT}}^{-1}\right]}^{\mathrm{y}}{\left[{\text{ML}}^{-3}\right]}^{\mathrm{z}}$
$=\left[{\text{M}}^{\mathrm{z}}{\text{L}}^{2\mathrm{x}+\mathrm{y}-3\mathrm{z}}{\text{T}}^{-\mathrm{y}}\right]$
This gives $\mathrm{z}=1,2\mathrm{x}+\mathrm{y}-3\mathrm{z}=1\text{ and }\mathrm{y}=2$
Solving we get X=1 ,Y= 2,and Z =1
$\therefore \mathrm{F}={\mathrm{AV}}^2\mathrm{P}$