Answer :

To find the cube root of [tex]\(27x^{18}\)[/tex], we need to look at both the numerical and variable parts separately.

1. Cube Root of the Numerical Coefficient:

The numerical coefficient given is 27. We need to find the cube root of 27.

[tex]\[
\sqrt[3]{27} = 3
\][/tex]

2. Cube Root of the Variable Part:

We have the variable part as [tex]\(x^{18}\)[/tex]. To find the cube root, we take the power and divide it by 3:

[tex]\[
\left(x^{18}\right)^{1/3} = x^{18/3} = x^6
\][/tex]

3. Combining Both Parts:

By combining the results from both steps, the cube root of [tex]\(27x^{18}\)[/tex] is:

[tex]\[
3x^6
\][/tex]

Therefore, the cube root of [tex]\(27x^{18}\)[/tex] is [tex]\(3x^6\)[/tex].

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