Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Get expert answers to your questions quickly and accurately from our dedicated community of professionals. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
Certainly! Let's break down and simplify the expression [tex]\(2 \sqrt[3]{27 x^3 y^6}\)[/tex] step-by-step.
### Step 1: Simplification Inside the Cube Root
First, we need to simplify the expression inside the cube root, [tex]\( \sqrt[3]{27 x^3 y^6} \)[/tex].
1. Cube Root of 27:
- We know that [tex]\( 27 = 3^3 \)[/tex]. Therefore, [tex]\( \sqrt[3]{27} = 3 \)[/tex] since [tex]\( 3^3 = 27 \)[/tex].
2. Cube Root of [tex]\( x^3 \)[/tex]:
- The cube root of [tex]\( x^3 \)[/tex] is [tex]\( x \)[/tex] because [tex]\( (x^3)^{1/3} = x \)[/tex].
3. Cube Root of [tex]\( y^6 \)[/tex]:
- The cube root of [tex]\( y^6 \)[/tex] can be simplified as follows: [tex]\( (y^6)^{1/3} = y^{6/3} = y^2 \)[/tex].
Combining these results, we have:
[tex]\[ \sqrt[3]{27 x^3 y^6} = 3 \cdot x \cdot y^2 \][/tex]
### Step 2: Multiply by 2
Next, we need to multiply the simplified result inside the cube root by 2:
[tex]\[ 2 \cdot \sqrt[3]{27 x^3 y^6} = 2 \cdot (3 \cdot x \cdot y^2) \][/tex]
Perform the multiplication:
[tex]\[ 2 \cdot 3 \cdot x \cdot y^2 = 6 x y^2 \][/tex]
### Final Answer
Thus, the simplified form of the expression [tex]\( 2 \sqrt[3]{27 x^3 y^6} \)[/tex] is:
[tex]\[ 6 x y^2 \][/tex]
So, the answer is:
[tex]\[ 6 x y^2 \][/tex]
### Step 1: Simplification Inside the Cube Root
First, we need to simplify the expression inside the cube root, [tex]\( \sqrt[3]{27 x^3 y^6} \)[/tex].
1. Cube Root of 27:
- We know that [tex]\( 27 = 3^3 \)[/tex]. Therefore, [tex]\( \sqrt[3]{27} = 3 \)[/tex] since [tex]\( 3^3 = 27 \)[/tex].
2. Cube Root of [tex]\( x^3 \)[/tex]:
- The cube root of [tex]\( x^3 \)[/tex] is [tex]\( x \)[/tex] because [tex]\( (x^3)^{1/3} = x \)[/tex].
3. Cube Root of [tex]\( y^6 \)[/tex]:
- The cube root of [tex]\( y^6 \)[/tex] can be simplified as follows: [tex]\( (y^6)^{1/3} = y^{6/3} = y^2 \)[/tex].
Combining these results, we have:
[tex]\[ \sqrt[3]{27 x^3 y^6} = 3 \cdot x \cdot y^2 \][/tex]
### Step 2: Multiply by 2
Next, we need to multiply the simplified result inside the cube root by 2:
[tex]\[ 2 \cdot \sqrt[3]{27 x^3 y^6} = 2 \cdot (3 \cdot x \cdot y^2) \][/tex]
Perform the multiplication:
[tex]\[ 2 \cdot 3 \cdot x \cdot y^2 = 6 x y^2 \][/tex]
### Final Answer
Thus, the simplified form of the expression [tex]\( 2 \sqrt[3]{27 x^3 y^6} \)[/tex] is:
[tex]\[ 6 x y^2 \][/tex]
So, the answer is:
[tex]\[ 6 x y^2 \][/tex]
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.