If you need to understand how a lot $3^{100}$ is, you’ll be able to simply kind it into a pc and it’ll spit out a very massive quantity. But that’s no enjoyable. The activity is to estimate $3^{100}$ with some computation which may be checked and adopted with out laptop help and that may be written down on at most one sheet of paper (theoretically one might compute the precise quantity on paper however that’s no enjoyable both and definitely would not match on a single sheet).

Answers needs to be within the type of scientific notation (one thing like $3.45 cdot 10^{7}$) and be inside $pm 50%$ of the precise worth which my laptop tells me is round

$5.15377*10^{47}$

however simply getting the proper variety of digits is already non trivial.