Answer :
Sure! Let's solve the problem step by step to find the cube root of [tex]\(27x^{18}\)[/tex].
1. Find the cube root of 27:
- The number 27 is a perfect cube, as [tex]\(27 = 3 \times 3 \times 3 = 3^3\)[/tex].
- Therefore, the cube root of 27 is 3.
2. Find the cube root of [tex]\(x^{18}\)[/tex]:
- When finding the cube root of a variable expression like [tex]\(x^{18}\)[/tex], we divide the exponent by 3.
- So, the cube root of [tex]\(x^{18}\)[/tex] is [tex]\(x^{18/3} = x^6\)[/tex].
3. Combine the results:
- We multiply the cube root of the numerical part by the cube root of the variable expression.
- This gives us [tex]\(3 \times x^6\)[/tex].
Therefore, the cube root of [tex]\(27x^{18}\)[/tex] is [tex]\(3x^6\)[/tex].
The correct choice is [tex]\(3x^6\)[/tex].
1. Find the cube root of 27:
- The number 27 is a perfect cube, as [tex]\(27 = 3 \times 3 \times 3 = 3^3\)[/tex].
- Therefore, the cube root of 27 is 3.
2. Find the cube root of [tex]\(x^{18}\)[/tex]:
- When finding the cube root of a variable expression like [tex]\(x^{18}\)[/tex], we divide the exponent by 3.
- So, the cube root of [tex]\(x^{18}\)[/tex] is [tex]\(x^{18/3} = x^6\)[/tex].
3. Combine the results:
- We multiply the cube root of the numerical part by the cube root of the variable expression.
- This gives us [tex]\(3 \times x^6\)[/tex].
Therefore, the cube root of [tex]\(27x^{18}\)[/tex] is [tex]\(3x^6\)[/tex].
The correct choice is [tex]\(3x^6\)[/tex].
