Here’s a thread with some discussion of that question.

Note that it looks like the LaTeX plugin somehow failed for you. Here’s how those equations should have rendered:

z^{(i)} = Wavg^{(i)} + b

a^{(i)} = softmax(z^{(i)})

\mathcal{L}^{(i)} = - \displaystyle \sum_{k = 0}^{n_y - 1} Y_{oh,k}^{(i)} * log(a^{(i)}_k)

With the information in that thread I referenced above, you should be able to decode which operations are dot products and which are elementwise.