Q. 45 - Intermediate Algebra

Question

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

$ⓐ \sqrt[3]{216a^6} ⓑ \sqrt[5]{32b^{20}}$

Step-by-Step Solution

Answer

Part(a)$\sqrt[3]{216a^6}=6a^2$

Part(b)$\sqrt[5]{32b^{20}}=2b^4$

Part(a) Step 1. Given information

Simplify using absolute values as necessary. 

$ⓐ \sqrt[3]{216a^6}$

Step 2. Explanaiton

$\begin{array}{l}\text{Since }\\ \Rightarrow 216a^6={\left(6a^2\right)}^3\\ \Rightarrow \sqrt[3]{216a^6}\\ \Rightarrow \sqrt[3]{{\left(6a^2\right)}^3}\\ \Rightarrow 6a^2\end{array}$

Part(b) Step 1. Given informaiton

$ⓑ \sqrt[5]{32b^{20}}$

Simplify using absolute values as necessary. 

Step 2. Explanation

$\begin{array}{l}\text{Since }\\ \Rightarrow 32b^{20}={\left(2b^4\right)}^5\\ \Rightarrow \sqrt[5]{32b^{20}}\\ \Rightarrow \sqrt[5]{{\left(2b^4\right)}^5}\\ \Rightarrow 2b^4\end{array}$