If force [ F ] , acceleration [ A ] and time [ T ] are chosen as...

Let consider,

$[ Energy ] = [ F{]}^{a} [ A{]}^{b} [ T{]}^{c}$

Now put the dimensional formula of the given quantities,

\left[{ML}^{2}{T}^{- 2}\right] = {\left[{MLT}^{- 2}\right]}^{a}{\left[{LT}^{- 2}\right]}^{b} [ T{]}^{c}$</p><p>\left[{ML}^{2}{T}^{- 2}\right] = \left[{M}^{a}{L}^{a + b}{T}^{- 2a - 2b + c}\right]$

On comparing powers of $[ M ]$

$a = 1$

On comparing powers of $[ L ]$

$a + b = 2$

$⇒ 1 + b = 2$

$⇒ b = 1$

On comparing powers of $[ T ]$

$- 2a - 2b + c = - 2$

$⇒ - 2 - 2 + c = - 2$

$⇒ c = 2$

$[ Energy ] = [ F ] [ A ] \left[{T}^{2}\right]