Chapter A.1, Problem 80E

Solution

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

  $\sqrt[3]{{(-2)}^3}>-2$ .

Given:

The given statement is $\sqrt[3]{{(-2)}^3}$ $\left|\right|$ $-2$ .

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 $\sqrt[3]{{(-2)}^3}$ $\left|\right|$ $-2$ .

  ${(-a)}^n=a^n$ if n is even

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

  $\sqrt[3]{{(-2)}^3}>-2$

Therefore $\sqrt[3]{{(-2)}^3}>-2$

Thus $\sqrt[3]{{(-2)}^3}$ is greater than -2.