Velocity of light, [c]=[LT−1] Gravitational constant, [G]=[M−1L3T−2] Planck's constant, [h]=[ML2T−1] Let dimensions of density d in new system are d=ca,Gb,hc Then expressing both sides in terms of dimensions of fundamental units, we get [ML−3]=[LT−1]a[M−1L3T−2]b[ML2T−1]c ⇒[ML−3]=[M−b+cLa+3b+2cT−a−2b−c] Comparing both sides we get, −b+c=1....(i) a+3b+2c=−3...(ii) and −a−2b−c=0...(iii) Solving these we get, a=5,b=−2,c=−1 So, density can be expressed as d=c5G−2h−1