The potential energy of a particle varies with distance x as U=Ax1/2x2+B, where A and B are constants. The dimensional formula for A x B is
M1L7/2T−2
M1L11/2T−2
M1L5/2T−2
M1L9/2T−2
Here x2 has the dimensions of L2,B=L2 Also ML2T−2=AL1/2L2 or A=ML7/2T−2∴ A×B=ML11/2T−2