Part A

What are the dimensions of density, which is mass per volume? The dimensions of mass and length are abbreviated as [M] and [L] respectively.

Mass is easy to represent as simply [M]

Volume is a quantity that exists only within 3 spatial dimensions. We'll need to take the cube of [L], which gives volume a dimension of [L]³

Density is mass divided by volume, therefore divide [M] by [L]³

The dimension of density is [M]/[L]³ or [M][L]⁻³