Q. 44 - Intermediate Algebra

Question

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

$ⓐ \sqrt[3]{-8c^9} ⓑ \sqrt[3]{125d^{15}}$

Step-by-Step Solution

Answer

Part(a)$\sqrt[3]{-8c^9}=-2c^2$

Part(b)$\sqrt[3]{125d^{15}} =5d^5$

Part(a) Given inormaiton

$ⓐ \sqrt[3]{-8c^9}$

 Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l}\text{Since }\\ \Rightarrow 8c^9={\left(2c^3\right)}^3\\ \Rightarrow \sqrt[3]{-8c^9}\\ \Rightarrow \sqrt[3]{{\left(-2c^3\right)}^3}\\ \Rightarrow -2c^3\end{array}$

Part(b) Step 1. Given information

$ⓑ \sqrt[3]{125d^{15}}$

 Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l}\text{Since }\\ \Rightarrow 125d^{15}={\left(5d^5\right)}^3\\ \Rightarrow \sqrt[3]{125d^{15}}\\ \Rightarrow \sqrt[3]{{\left(5d^5\right)}^3}\\ \Rightarrow 5d^5\end{array}$