Chapter 8.3, Problem 60ES

To determine

(a)

The set of numbers $\left\{2^k\right\}$, where $k$ is an integer, form a group with multiplication as the operation. Which element of the group is the identity element?

To determine

(b)

The set of numbers $\left\{2^k\right\}$, where $k$ is an integer, form a group with multiplication as the operation. Verify that the set is closed with respect to multiplication

To determine

(c)

The set of numbers $\left\{2^k\right\}$, where $k$ is an integer, form a group with multiplication as the operation. Which element is the inverse of $2^8$

To determine

(d)

The set of numbers $\left\{2^k\right\}$, where $k$ is an integer, form a group with multiplication as the operation. Which element is the inverse of $\frac{1}{32}$ ?

To determine

(c)

The set of numbers $\left\{2^k\right\}$, where $k$ is an integer, form a group with multiplication as the operation. Which element is the inverse of $2^k$ ?