**Simplifying Radical Expressions: Worked Example**In this example, we aim to simplify the radical expression \( \sqrt[3]{32k^4} \). Follow along to see each step of the process and where errors might occur.### Step-by-step Solution:1. **Initial Expression**: \[ \sqrt[3]{32k^4} \] 2. **Incorrect First Attempt**: \[ \sqrt[3]{k \times \boxed{\phantom{x}}} \cdot 4k \quad \textcolor{red}{\text{(Incorrect)}} \]3. **Second Attempt**: \[ \sqrt[3]{k \times \boxed{\phantom{x}}} \times \sqrt[3]{4k} \quad \textcolor{red}{\text{(Incorrect)}} \]4. **Third Attempt**: \[ 2k \sqrt[3]{k \times \boxed{\phantom{x}}} \quad \textcolor{red}{\text{(Incorrect)}} \]### Points to Note:- Each step tried to decompose or simplify the original expression differently.- Each step is marked with a red "X" indicating it is incorrect.**Key Concepts to Correct Solutions**:1. Recognize that \( 32k^4 \) can be written in the form \( 32 \cdot k^4 \).2. Break down \( 32 \) into a power of 2: \( 32 = 2^5 \).3. Use the property of radicals: \( \sqrt[3]{a \cdot b} = \sqrt[3]{a} \cdot \sqrt[3]{b} \).4. Recognize the simplification inside the cube root.Correct Simplification Steps:\[\sqrt[3]{32k^4} = \sqrt[3]{2^5 \cdot k^4} = \sqrt[3]{2^5} \cdot \sqrt[3]{k^4}\]\[\sqrt[3]{2^5} = 2 \sqrt[3]{2^2}\]\[\sqrt[3]{k^4} = k \cdot \sqrt[3]{k}\]\[\therefore \sqrt[

Name: **Simplifying Radical Expressions: Worked Example**In this example, w
Uploaded: 2024-03-20T06:46:03.000Z
Channel: Bartleby
Description: **Simplifying Radical Expressions: Worked Example**In this example, we aim to simplify the radical expression \( \sqrt[3]{32k^4} \). Follow along to see each step of the process and where errors might occur.### Step-by-step Solution:1. **Initial Exp