Question

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

$ⓐ\sqrt[8]{k^8}ⓑ\sqrt[6]{p^6}$

Short answer

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

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

Step-by-step solution

Part(a) Step 1. Given information

$ⓐ\sqrt[8]{k^8}$

Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l}\text{Sincetheindexniseven},\sqrt[n]{a^n}=\left|a\right|.\\ \text{Heren=8isanevennumber}\\ \sqrt[8]{k^8}=\left|k\right|\end{array}$

Part(b) Step 1. Given information

$ⓑ\sqrt[6]{p^6}$

Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l}\text{Weusetheabsolutevaluetobesuretogetthepositiveroot.}\\ \text{Sincetheindexniseven},\sqrt[n]{a^n}=\left|a\right|.\\ \text{Heren=6isanevennumber}\\ \sqrt[6]{p^6}=\left|p\right|\end{array}$