Physics - Unit & Dimension Question with Solution | TestHub

$[M{]}^1=[V{]}^a\left[T{]}^b\right[F{]}^c$
$[M{]}^1={\left[L{T}^{-1}\right]}^a[T{]}^b{\left[ML{T}^{-2}\right]}^c$
$[M{]}^1=[M{]}^c\left[L{]}^{a+c}\right[T{]}^{-a+b-2c}$
Thus,

$\begin{array}{ccc}c=1,& a+c=0 \text{and}& b-a-2c=0\\ & \Rightarrow a=-1& \Rightarrow b=-1+2=1\end{array}$
Thus, $\left[M\right]=\left[V{]}^{-1}\right[ T{]}^1[ F{]}^1$