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

$\left[ {M{L^0}{T^0}} \right] = \left[ {{M^a}{L^{a + b}}{T^{ - 2ab + c}}} \right]$
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. $(i),\,\left[ m \right] = \left[ {F{V^{ - 1}}T} \right]$