d
Let, mass, m,  \(\propto \,{F^a}{V^b}{T^e}\)
or,  m\( = k{F^a}{V^b}{T^c}\)  ....................(\(i\))
Where k is a dimensionless constant and a, b and c are the exponents
Writing dimension on both sides we get

\(\left[ {M{L^0}{T^0}} \right] = {\left[ {ML{T^{ - 2}}} \right]^a}{\left[ {L{T^{ - 1}}} \right]^b}{\left[ T \right]^c}\)

\(\left[ {M{L^0}{T^0}} \right] = \left[ {{M^a}{L^{a + b}}{T^{ - 2ab + c}}} \right]\)
Applying the principle of homogeneity of

dimension we get

\(a=1\)     ..................(\(ii\))

\(a + b = 0\)         ........................(\(iii\))

\(- 2a - b + c = 0\)     ....................(\(iv\))
Solving eqns.,(\(ii\)), (\(iii\)), and (\(iv\)), we get
\(a = 1,b =  - 1,c = 1\)
From eqn. \((i),\,\left[ m \right] = \left[ {F{V^{ - 1}}T} \right]\)