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Answer :
To find the cube root of [tex]\(8x^{27}\)[/tex], we can break it into two parts: the cube root of the number and the cube root of the variable expression.
1. Cube Root of 8:
- The cube root of 8 is 2 because [tex]\(2^3 = 8\)[/tex].
2. Cube Root of [tex]\(x^{27}\)[/tex]:
- To find the cube root of [tex]\(x^{27}\)[/tex], you take the exponent 27 and divide it by 3.
- So, [tex]\((x^{27})^{1/3} = x^{27/3} = x^9\)[/tex].
Now, combine both parts:
- The cube root of [tex]\(8x^{27}\)[/tex] is [tex]\(2 \times x^9\)[/tex], which simplifies to [tex]\(2x^9\)[/tex].
Thus, the correct answer is [tex]\(2x^9\)[/tex].
1. Cube Root of 8:
- The cube root of 8 is 2 because [tex]\(2^3 = 8\)[/tex].
2. Cube Root of [tex]\(x^{27}\)[/tex]:
- To find the cube root of [tex]\(x^{27}\)[/tex], you take the exponent 27 and divide it by 3.
- So, [tex]\((x^{27})^{1/3} = x^{27/3} = x^9\)[/tex].
Now, combine both parts:
- The cube root of [tex]\(8x^{27}\)[/tex] is [tex]\(2 \times x^9\)[/tex], which simplifies to [tex]\(2x^9\)[/tex].
Thus, the correct answer is [tex]\(2x^9\)[/tex].
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