We study on computer simulations to infer a network structure of the hippocampal CA3 culture slice, which is not yet found even in physiological experiments. In order to find the network structure, we have to understand dynamical mechanisms of how to establish two power law distributions of spontaneous activities observed in the CA3 cultured slice. The first power law is the probabilistic distribution of firing frequency in a neuron. The second is of synchrony size that means a rate of co-active neurons within a time bin. In this work, we show that the power law observations significantly rely on the two network mechanisms: (1) high-frequency firing of interneurons by feedback from pyramidal cells, (2) log-normal distribution of synaptic weights.