2. Which of the following is the largest: $1^{20}, 2^{14}, 4^{8}, 8^{5}, 16^{3}$ ?
2. Since $1^{20}=1$ and each of the other numbers is larger than 1 , then $1^{20}$ is not the largest of the numbers.
We convert the last three numbers to powers of 2 , using the rule that $\left(2^{a}\right)^{b}=2^{a b}$ :
$$
4^{8}=\left(2^{2}\right)^{8}=2^{16} \quad 8^{5}=\left(2^{3}\right)^{5}=2^{15} \quad 16^{3}=\left(2^{4}\right)^{3}=2^{12}
$$

Therefore, the numbers in the list are $1,2^{14}, 2^{16}, 2^{15}, 2^{12}$.
Since the bases of the last four numbers are equal and this base is larger than 1 , then the largest number is the one with the largest exponent.
Therefore, $4^{8}=2^{16}$ is the largest number in the list.
(We could have used a calculator to calculate the five numbers to be $1,16384,65536,32764,4096$.)
ANSWER: $4^{8}=2^{16}=65536$