Right option is (a) \(\frac{1}{s^{100}}\)
To elaborate: n times = u (t) * u (t) * …… * u (t)
Laplace transform of the above function = \(\frac{1}{s^n}\), where n is number of convolutions.
∴ Laplace transform for 100 convolutions = \(\frac{1}{s^{100}}\).