Q. 28 - Intermediate Algebra

Question

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

$ⓐ \sqrt[3]{a^3} ⓑ \sqrt[9]{b^9}$

Step-by-Step Solution

Answer

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

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

Part(a) Srep1. Given information

$ⓐ \sqrt[3]{a^3}$

Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l}\text{This is an odd indexed root so there is no need for an absolute value sign.}\\ \text{Since the index n is odd},\sqrt[n]{a^n}=a.\\ \text{Here n = 3 odd number}\\ \sqrt[3]{a^3}=a\end{array}$

Part(b) Step 1. Given information

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

Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l}\text{This is an odd indexed root so there is no need for an absolute value sign.}\\ \text{Since the index n is odd},\sqrt[n]{a^n}=a.\\ \text{Here n = 9 odd number}\\ \sqrt[9]{b^9}=b\end{array}$