In my attempts to learn linear algebra from Khan Academy I've come across several concepts that I can't completely connect.
Every vector space has a base. This base consists of the minimal elements that can span the entire vector space.
The number of elements in this vector space is defined to be the vector space's dimension.
When trying to conclude the power of a vector space (as in how many vectors there are in the space), I know that $|V| = |F| ^ n$
I also know that this small n = dimension of V. What I don't understand is why does the dimension equals that $n$?