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Answer :
To find the cube root of the expression [tex]\(27x^{18}\)[/tex], we break the process into manageable steps.
1. Cube Root of the Number 27:
- The cube root of 27 is 3 because [tex]\(3 \times 3 \times 3 = 27\)[/tex].
2. Cube Root of the Variable Expression [tex]\(x^{18}\)[/tex]:
- When you take the cube root of [tex]\(x^{18}\)[/tex], you're actually finding [tex]\((x^{18})^{1/3}\)[/tex].
- This can be calculated by dividing the exponent by 3:
[tex]\[
x^{18/3} = x^6
\][/tex]
3. Combine the Results:
- Now, combine the cube root of the number and the cube root of the variable part.
- This gives us: [tex]\(3x^6\)[/tex].
Therefore, the cube root of [tex]\(27x^{18}\)[/tex] is [tex]\(3x^6\)[/tex], which matches the answer [tex]\(3x^6\)[/tex] from the given options.
1. Cube Root of the Number 27:
- The cube root of 27 is 3 because [tex]\(3 \times 3 \times 3 = 27\)[/tex].
2. Cube Root of the Variable Expression [tex]\(x^{18}\)[/tex]:
- When you take the cube root of [tex]\(x^{18}\)[/tex], you're actually finding [tex]\((x^{18})^{1/3}\)[/tex].
- This can be calculated by dividing the exponent by 3:
[tex]\[
x^{18/3} = x^6
\][/tex]
3. Combine the Results:
- Now, combine the cube root of the number and the cube root of the variable part.
- This gives us: [tex]\(3x^6\)[/tex].
Therefore, the cube root of [tex]\(27x^{18}\)[/tex] is [tex]\(3x^6\)[/tex], which matches the answer [tex]\(3x^6\)[/tex] from the given options.
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