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Answer :
To find the cube root of [tex]\(8x^{27}\)[/tex], let's break it down step-by-step:
1. Cube root of 8:
The cube root of 8 is the number that, when multiplied by itself three times, gives 8.
[tex]\[
\text{Cube root of } 8 = 2, \text{ because } 2^3 = 8.
\][/tex]
2. Cube root of [tex]\(x^{27}\)[/tex]:
When taking the cube root of a power, you divide the exponent by 3.
[tex]\[
\text{Cube root of } x^{27} = x^{27/3} = x^9.
\][/tex]
3. Combine the results:
To find the cube root of the entire expression [tex]\(8x^{27}\)[/tex], we multiply the cube roots of each part.
[tex]\[
\text{Cube root of } 8x^{27} = 2 \times x^9 = 2x^9.
\][/tex]
So, the cube root of [tex]\(8x^{27}\)[/tex] is [tex]\(2x^9\)[/tex].
Therefore, the correct choice is [tex]\(2x^9\)[/tex].
1. Cube root of 8:
The cube root of 8 is the number that, when multiplied by itself three times, gives 8.
[tex]\[
\text{Cube root of } 8 = 2, \text{ because } 2^3 = 8.
\][/tex]
2. Cube root of [tex]\(x^{27}\)[/tex]:
When taking the cube root of a power, you divide the exponent by 3.
[tex]\[
\text{Cube root of } x^{27} = x^{27/3} = x^9.
\][/tex]
3. Combine the results:
To find the cube root of the entire expression [tex]\(8x^{27}\)[/tex], we multiply the cube roots of each part.
[tex]\[
\text{Cube root of } 8x^{27} = 2 \times x^9 = 2x^9.
\][/tex]
So, the cube root of [tex]\(8x^{27}\)[/tex] is [tex]\(2x^9\)[/tex].
Therefore, the correct choice is [tex]\(2x^9\)[/tex].
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