Answer :
To find the cube root of the expression [tex]\(8x^{27}\)[/tex], let's break it down step by step:
1. Cube Root of 8:
- The cube root of 8 is a number that, when multiplied by itself three times, gives 8.
- We know that [tex]\(2 \times 2 \times 2 = 8\)[/tex].
- Thus, the cube root of 8 is 2.
2. Cube Root of [tex]\(x^{27}\)[/tex]:
- When taking the cube root of [tex]\(x^{27}\)[/tex], you divide the exponent by 3.
- So, [tex]\(\frac{27}{3} = 9\)[/tex].
3. Combine the Results:
- Combine the cube root of the numerical part and the cube root of the variable part.
- The cube root of [tex]\(8x^{27}\)[/tex] is [tex]\(2x^9\)[/tex].
Therefore, the correct option is [tex]\(\boxed{2x^9}\)[/tex].
1. Cube Root of 8:
- The cube root of 8 is a number that, when multiplied by itself three times, gives 8.
- We know that [tex]\(2 \times 2 \times 2 = 8\)[/tex].
- Thus, the cube root of 8 is 2.
2. Cube Root of [tex]\(x^{27}\)[/tex]:
- When taking the cube root of [tex]\(x^{27}\)[/tex], you divide the exponent by 3.
- So, [tex]\(\frac{27}{3} = 9\)[/tex].
3. Combine the Results:
- Combine the cube root of the numerical part and the cube root of the variable part.
- The cube root of [tex]\(8x^{27}\)[/tex] is [tex]\(2x^9\)[/tex].
Therefore, the correct option is [tex]\(\boxed{2x^9}\)[/tex].
