If force $\text{'}F\text{'},$ acceleration $\text{'}A\text{'}$ and time $\text{'}T\text{'}$ are taken as fundamental quantities then the dimensions of energy are.

$$\begin{gathered} E\alpha F^a{A}^b{T}^c \\ M{L}^2{T}^{-2}=k{\left(ML{T}^{-2}\right)}^a.{\left(L{T}^{-2}\right)}^b{T}^c M{L}^2{T}^{-2}=k{M}^a{L}^{a+b}{T}^{-2a-2b+c} \\ Compare on both side M_{,}{L}_{,}T Dimensions \\ M\to a=1,a+b=2 \\ L\to b=2-1=1 \\ T\to -2a-2b+c=-2 \\ substitute a, b values \\ 2a+2b-c=2 \\ 2+2-c=2 \\ c=2 \\ E=F^{1}A{T}^2 \\ ALTERNATELY: \\ power =force \times velocity \\ \frac{energy}{time}=force\times acceleration\times time \\ so E=FA{T}^2 \end{gathered}$$