The dimensional formula of density is [M1L−3T0][M^1L^{-3}T^0][M1L−3T0].
Explanation
Density is defined as mass per unit volume. Mathematically,
Density=MassVolume\text{Density}=\frac{\text{Mass}}{\text{Volume}}Density=VolumeMass
The dimensional formula of mass is [M1L0T0][M^1L^0T^0][M1L0T0] and the dimensional formula of volume (which is length cubed) is [M0L3T0][M^0L^3T^0][M0L3T0]. Using these,
[Density]=[M1L0T0][M0L3T0]=[M1−0L0−3T0−0]=[M1L−3T0][\text{Density}]=\frac{[M^1L^0T^0]}{[M^0L^3T^0]}=[M^{1-0}L^{0-3}T^{0-0}]=[M^1L^{-3}T^0][Density]=[M0L3T0][M1L0T0]=[M1−0L0−3T0−0]=[M1L−3T0]
This indicates that density depends on mass raised to the power of 1, length raised to the power of -3, and is independent of time (time raised to the power of 0).
