Chapter A.1, Problem 78E

Solution

Replace | | with <, = , or > to make a true statement.

  ${(2^{-3})}^{1/3}<2$ .

Given:

The given statement is ${(2^{-3})}^{1/3}$ $\left|\right|$ $2$ .

Concept Used:

• The greater than symbol means the number on the left is greater than the number on the right.
• The greater than or equal symbol means the number on the left is greater than or equal to the number on the right.
• The less than symbol means that the number on the left is less than the number on the right.

Calculation:

The given statement is ${(2^{-3})}^{1/3}$ $\left|\right|$ $2$ .

  $\begin{array}{c}$ {(2^{-3})}^{1/3}=2^{\frac{-3}{3}}$=2^{-1}\\ =\frac{1}{2}\end{array}$

  ${(2^{-3})}^{1/3}<2$

Therefore ${(2^{-3})}^{1/3}<2$

Thus ${(2^{-3})}^{1/3}$ is less than 2.