Q. 46 - Intermediate Algebra

Question

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

$ⓐ \sqrt[7]{128r^{14}} ⓑ\sqrt[4]{81s^{24}}$

Step-by-Step Solution

Answer

Part(a)$\sqrt[7]{128r^{14}}=2r^2$

Part(b)$\sqrt[4]{81s^{24}}=3s^6$

Part(a) Step 1. Given information

$ⓐ \sqrt[7]{128r^{14}}$

 Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l}\text{Since}\\ \Rightarrow 128r^{14}={\left(2r^2\right)}^7\\ \Rightarrow \sqrt[7]{128r^{14}}\\ \Rightarrow \sqrt[7]{{\left(2r^2\right)}^7}\\ \Rightarrow 2r^2\end{array}$

Part(b) Step 1. Given information

$ⓑ\sqrt[4]{81s^{24}}$

 Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l}\text{Since}\\ \Rightarrow 81s^{24}={\left(3s^6\right)}^4\\ \Rightarrow \sqrt[4]{81s^{24}}\\ \Rightarrow \sqrt[4]{{\left(3s^6\right)}^4}\\ \Rightarrow 3s^6\\ \Rightarrow \sqrt[4]{81s^{24}}=3s^6\end{array}$