It is the result of scalar multiplication by the scalar 0 (here meaning the additive identity of the underlying field, not necessarily the real number 0).
The set of all geometrical vectors, together with the operations of vector addition and scalar multiplication, satisfies all the axioms of a vector space.
When measurable quantities are raised to a rational power, the same is done to the dimensional symbols attached to those quantities; this corresponds to scalar multiplication in the vector space.
