Q. 30 - Intermediate Algebra

Question

In the following exercises, simplify using absolute values as necessary. 

$ⓐ \sqrt[8]{k^8} ⓑ \sqrt[6]{p^6}$

Step-by-Step Solution

Answer

Part(a)$\sqrt[8]{k^8}=\left|k\right|$

Part(b)$\sqrt[6]{p^6}=\left|p\right|$

Part(a) Step 1. Given information

$ⓐ \sqrt[8]{k^8}$

 Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l}\text{Since the index n is even},\sqrt[n]{a^n}=\left|a\right|.\\ \text{Here n=8 is an even number}\\ \sqrt[8]{k^8}=\left|k\right|\end{array}$

Part(b) Step 1. Given information

$ⓑ \sqrt[6]{p^6}$

 Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l}\text{We use the absolute value to be sure to get the positive root.}\\ \text{Since the index n is even},\sqrt[n]{a^n}=\left|a\right|.\\ \text{Here n=6 is an even number}\\ \sqrt[6]{p^6}=\left|p\right|\end{array}$