text: # How do you simplify (root3(-162x^6))?
  
  Oct 3, 2015
  
  $\sqrt[3]{- 162 {x}^{6}} = {x}^{2} \left(- 3 \sqrt[3]{6}\right)$
  
  #### Explanation:
  
  We can take a minus out of the root, because $- 1 = {\left(- 1\right)}^{3}$
  
  $- \sqrt[3]{162 {x}^{6}}$
  
  We know that ${x}^{6} = {x}^{2} \cdot {x}^{2} \cdot {x}^{2}$ or ${x}^{6} = {\left({x}^{2}\right)}^{3}$, so we can take a ${x}^{2}$ out of the root
  
  $- {x}^{2} \sqrt[3]{162}$
  
  Lastly, all we have to do is factor the $162$, so
  
  $162 | 2$
  $\textcolor{w h i t e}{0} 81 | 3$
  $\textcolor{w h i t e}{0} 27 | 3$
  $\textcolor{w h i t e}{00} 9 | 3$
  $\textcolor{w h i t e}{00} 3 | 3$
  $\textcolor{w h i t e}{00} 1 | 2 \cdot {3}^{4}$
  
  So we can take a $3$ out of the root, leaving a $2 \cdot 3$, that is, $6$ inside it. So
  
  $\sqrt[3]{- 162 {x}^{6}} = {x}^{2} \left(- 3 \sqrt[3]{6}\right)$
explanation: The document contains a math question and its corresponding answer. The question asks how to simplify the expression \(\sqrt[3]{-162x^6}\), and the answer provides a step-by-step explanation of the simplification process.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # How do you simplify (root3(-162x^6))?
  
  Oct 3, 2015
  
  $\sqrt[3]{- 162 {x}^{6}} = {x}^{2} \left(- 3 \sqrt[3]{6}\right)$
  
  #### Explanation:
  
  We can take a minus out of the root, because $- 1 = {\left(- 1\right)}^{3}$
  
  $- \sqrt[3]{162 {x}^{6}}$
  
  We know that ${x}^{6} = {x}^{2} \cdot {x}^{2} \cdot {x}^{2}$ or ${x}^{6} = {\left({x}^{2}\right)}^{3}$, so we can take a ${x}^{2}$ out of the root
  
  $- {x}^{2} \sqrt[3]{162}$
  
  Lastly, all we have to do is factor the $162$, so
  
  $162 | 2$
  $\textcolor{w h i t e}{0} 81 | 3$
  $\textcolor{w h i t e}{0} 27 | 3$
  $\textcolor{w h i t e}{00} 9 | 3$
  $\textcolor{w h i t e}{00} 3 | 3$
  $\textcolor{w h i t e}{00} 1 | 2 \cdot {3}^{4}$
  
  So we can take a $3$ out of the root, leaving a $2 \cdot 3$, that is, $6$ inside it. So
  
  $\sqrt[3]{- 162 {x}^{6}} = {x}^{2} \left(- 3 \sqrt[3]{6}\right)$
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and its corresponding answer. The question asks how to simplify the expression \(\sqrt[3]{-162x^6}\), and the answer provides a step-by-step explanation of the simplification process.
  
  Label: question-and-answer