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].

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