Q. 81 - Intermediate Algebra

Question

In the following exercises, simplify using absolute value signs as needed.

$$\begin{gathered} a. \sqrt[5]{-32} \\ b. \sqrt[8]{-1} \end{gathered}$$ 

Step-by-Step Solution

Answer

The simplified expressions are,

$a. -2$

b. Not a real number.

Step 1 Given expressions are,

$$\begin{gathered} a. \sqrt[5]{-32} \\ b. \sqrt[8]{-1} \end{gathered}$$

The objective is, we need to find the simplified expressions for the given expressions.

The product property for the root is,

$\sqrt[n]{ab}=\sqrt[n]{a}.\sqrt[n]{b}$ and $\sqrt[n]{a}.\sqrt[n]{b}=\sqrt[n]{ab}$

Part a Step 2 - 32 5 .

$$\begin{gathered} \sqrt[5]{-32} =\sqrt[5]{{\left(-2\right)}^5} \\ =-2 \end{gathered}$$

Part b Step 2     - 1 8 = - 1 .

Because, there is not a perfect  power of the index $n$, where $n^8$is the no real number $-1$.

So, the answer is not a real number.