Consider two physical quantities A and B related to each other as E...

From the dimensional checking of the equation, we can say the dimensions of $\left[B\right] = \left[{x}^{2}\right] = \left[{L}^{2}\right]</p><p>And dimensions$ of \left[A\right] = \dfrac{\left[{x}^{2}\right]}{\left[tE\right]} = \dfrac{\left[{L}^{2}\right]}{\left[T\right]\left[M{L}^{2}{T}^{- 2}\right]} = \dfrac{1}{\left[M{T}^{- 1}\right]}

Hence, \left[A\right]$= \left[{M}^{- 1}T\right]$

Required value, \left[AB\right]$= \left[{L}^{2}{M}^{- 1}{T}^{1}\right]$