If force (F), velocity (V) and time (T) are taken as fundamental units, then the dimensions of mass are

If force (F), velocity (v) and time (T) are taken as fundamental quantities, mass can be written as

$\begin{array}{rl} & M=F^x{V}^y{T}^z\\ & M^{\mathrm{\prime }}{L}^0{T}^0={\left(ML{T}^{-2}\right)}^x{\left(L{T}^{-1}\right)}^y{T}^z\end{array}$

Where x, y, z are constants

$\begin{array}{ll}{M}^1=M^x& x=1\\ L^0=L^{x+y}x+y=0& x=-y,y=-1\\ T^0=T^{-2x-y+z}& 2x+y-z=0\\ & 2-1-z=0\\ & 1-z=0\\ & z=1\end{array}$

Hence, M = FT/V = F¹V^-1T¹.
Alternate method:
F x T = Change in momentum

$\begin{array}{rl} & \text{mass}=\frac{\text{momentum}}{\text{velocity}}\\ & =\frac{\mathrm{FT}}{\mathrm{V}}={\mathrm{FTV}}^{-1}\end{array}$