Explanation

Energy, $E \propto F^{a}A^{b}T^{c}$. $[E] = [F^{a}][A^{b}][T^{c}] \Rightarrow [ML^{2}T^{-2}] = [MLT^{-2}]^{a}[LT^{-2}]^{b}[T]^{c}$ $[ML^{2}T^{-2}] = [M^{a}L^{a+b}T^{-2a-2b+c}]$. Comparing dimensions on both sides. $a = 1$; $a + b = 2$ and $-2 = -2a - 2b + c$ $\therefore b = 1$ and $-2 = -2 - 2 + c$ or, $c = 2 \therefore$ Dimensions of energy = $[FAT^{2}]$