If momentum (p), area (A) and time (t) are taken to be fundamental quantities, then energy has the dimensional formula

Let energy E = kpaAbtc…..(i)Where k is a dimensionless constant of proportionality.Equating dimensions on both sides of (i), we get[ML2T-2]  = [MLT-1]a[M0L2T0]b[M0L0T]c                    = [ MaLa+2bTa+c]Applying the principle of homogeneity of dimensionswe geta = 1            …(ii)a+2b = 2 …(iii)-a+c =-2 …..(iv)On solving eqs. (ii), (iii) and (iv) we geta = 1, b = 12, c = -1∴{E] = [p1A12t-1]