Question

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

$ⓐ\sqrt[3]{a^3}ⓑ\sqrt[9]{b^9}$

Short answer

Part(a)$\sqrt[3]{a^3}=a$

Part(b)$\sqrt[9]{b^9}=b$

Step-by-step solution

Part(a) Srep1. Given information

$ⓐ\sqrt[3]{a^3}$

Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l}\text{Thisisanoddindexedrootsothereisnoneedforanabsolutevaluesign.}\\ \text{Sincetheindexnisodd},\sqrt[n]{a^n}=a.\\ \text{Heren=3oddnumber}\\ \sqrt[3]{a^3}=a\end{array}$

Part(b) Step 1. Given information

$\left(b\right)\sqrt[9]{b^9}$

Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l}\text{Thisisanoddindexedrootsothereisnoneedforanabsolutevaluesign.}\\ \text{Sincetheindexnisodd},\sqrt[n]{a^n}=a.\\ \text{Heren=9oddnumber}\\ \sqrt[9]{b^9}=b\end{array}$