A botanist is studying microsporogenesis and microgametogenesis in...

One microspore mother cell undergoes one meiotic division to produce four haploid microspores.

To produce $100$ microspores, the number of meiotic divisions required is $\dfrac{100}{4} = 25$.

Each microspore develops into a pollen grain. For the pollen to be shed at the $3$-celled stage, the microspore undergoes two mitotic divisions. The first mitotic division produces a vegetative cell and a generative cell. The second mitotic division occurs in the generative cell to produce two male gametes.

Since each of the $100$ microspores undergoes $2$ mitotic divisions, the total number of mitotic divisions required is $100 \times 2 = 200$.

Thus, $25$ meiotic and $200$ mitotic divisions are required.

Answer: 25 meiosis and 200 mitosis