The dimensions of ab in the equation P = a−t2bx2 where P is pressure, x is distance and t is time, are:
[M2L T–3]
[MLT–2]
[LT–3]
[ML3T-1]
P=a−t2bx2=abx2−t2bx2
As per principle of dimensional homogeneity each term in the equation must carry the dimension of pressure.
P=abx2⇒ab=Px2=ML−1T−2L2⇒ab=MLT−2