Answer :
Sure! Let's find the cube root of the expression [tex]\(8x^{27}\)[/tex].
### Step-by-Step Solution:
1. Understand the Problem:
We need to find the cube root of [tex]\(8x^{27}\)[/tex].
2. Break it Down:
- The expression inside the cube root is a product of two parts: the number [tex]\(8\)[/tex] and the variable term [tex]\(x^{27}\)[/tex].
3. Find the Cube Root of Each Part:
- Cube Root of the Number [tex]\(8\)[/tex]:
- The cube root of [tex]\(8\)[/tex] is [tex]\(2\)[/tex] because [tex]\(2^3 = 8\)[/tex].
- Cube Root of the Variable Term [tex]\(x^{27}\)[/tex]:
- To find the cube root of [tex]\(x^{27}\)[/tex], we divide the exponent by [tex]\(3\)[/tex].
- [tex]\(27 \div 3 = 9\)[/tex], so the cube root of [tex]\(x^{27}\)[/tex] is [tex]\(x^9\)[/tex].
4. Combine the Results:
- Now combine the cube roots of the two parts we found:
[tex]\[
2 \cdot x^9
\][/tex]
5. Conclusion:
The cube root of [tex]\(8x^{27}\)[/tex] is [tex]\(2x^9\)[/tex].
So, the correct answer is [tex]\(\boxed{2x^9}\)[/tex].
### Step-by-Step Solution:
1. Understand the Problem:
We need to find the cube root of [tex]\(8x^{27}\)[/tex].
2. Break it Down:
- The expression inside the cube root is a product of two parts: the number [tex]\(8\)[/tex] and the variable term [tex]\(x^{27}\)[/tex].
3. Find the Cube Root of Each Part:
- Cube Root of the Number [tex]\(8\)[/tex]:
- The cube root of [tex]\(8\)[/tex] is [tex]\(2\)[/tex] because [tex]\(2^3 = 8\)[/tex].
- Cube Root of the Variable Term [tex]\(x^{27}\)[/tex]:
- To find the cube root of [tex]\(x^{27}\)[/tex], we divide the exponent by [tex]\(3\)[/tex].
- [tex]\(27 \div 3 = 9\)[/tex], so the cube root of [tex]\(x^{27}\)[/tex] is [tex]\(x^9\)[/tex].
4. Combine the Results:
- Now combine the cube roots of the two parts we found:
[tex]\[
2 \cdot x^9
\][/tex]
5. Conclusion:
The cube root of [tex]\(8x^{27}\)[/tex] is [tex]\(2x^9\)[/tex].
So, the correct answer is [tex]\(\boxed{2x^9}\)[/tex].
