Chapter 10.3, Problem 3MS

The power of powers (H). In this section we discovered that the power of compounding arises from raising quantities to large powers. Which number is larger: $2^3\text{ or }{3}^2?4^5\text{or }{5}^4?$

In general, if n and m are large numbers and n exceeds m, which would you guess is loarger, $m^{n}or{n}^m?$

If you like money, would you rather have $\$2^{100}or{\text{ \$100}}^{\text{2}}?$