Chapter 6.1, Problem 9OE

To determine

To simplify: The given expression and identify if the expression represents the real number.

Answer to Problem 9OE

The simplified value of the given expression is $-13$ . The number $-13$ is the real number.

Explanation of Solution

Given:

The given expression is

  ${\left(-\sqrt[3]{13}\right)}^3$

Calculation:

The given expression can be simplified as follows.

  $\begin{array}{l}={\left(-\sqrt[3]{13}\right)}^3\\ ={\left(-1\right)}^3\times {13}^{3\times \frac{1}{3}}\\ =-13\end{array}$

Any number measurable on the number line whether positive, negative, and decimal or in fractions is called the real number.

Here, $-13$ is the real number.

Therefore, the simplified value of the given expression is $-13$ . The number $-13$ is the real number.