Solution:
A is the correct option.
Explanation:
We have to find the cube root of [tex]27x^{18}[/tex]
In order to find the cube root of the expression, we find the factors of 27.
[tex]27= 3 \times 3\times 3= 3^3[/tex]
Also x^18 can be written as
[tex]x^{18}=(x^6)^3[/tex]
Replace the given expression with these values, we get
[tex]\sqrt[3]{27x^{18}} =\sqrt[3]{3^3 \cdot (x^6)^3 }[/tex]
Now, we have the formula,
[tex]\sqrt[n]{x^n} =x[/tex]
Using this formula, the cube with the cube root got cancelled and we are left with
[tex]\sqrt[3]{27x^{18}} = 3\cdot x^6[/tex]
Therefore, the cube root of 27x^18 is 3x^6.
A is the correct option.
