Answer :
We start with the expression
[tex]$$
\sqrt[3]{27 x^{18}}.
$$[/tex]
This expression can be separated into the cube root of a product:
[tex]$$
\sqrt[3]{27 x^{18}} = \sqrt[3]{27} \cdot \sqrt[3]{x^{18}}.
$$[/tex]
First, notice that
[tex]$$
27 = 3^3,
$$[/tex]
so its cube root is
[tex]$$
\sqrt[3]{27} = 3.
$$[/tex]
Next, for the variable part, we use the property of exponents for radicals:
[tex]$$
\sqrt[3]{x^{18}} = x^{\frac{18}{3}} = x^6.
$$[/tex]
Thus, the entire expression simplifies to
[tex]$$
\sqrt[3]{27 x^{18}} = 3 \cdot x^6 = 3 x^6.
$$[/tex]
Therefore, the cube root of [tex]$27x^{18}$[/tex] is [tex]$\boxed{3 x^6}$[/tex].
[tex]$$
\sqrt[3]{27 x^{18}}.
$$[/tex]
This expression can be separated into the cube root of a product:
[tex]$$
\sqrt[3]{27 x^{18}} = \sqrt[3]{27} \cdot \sqrt[3]{x^{18}}.
$$[/tex]
First, notice that
[tex]$$
27 = 3^3,
$$[/tex]
so its cube root is
[tex]$$
\sqrt[3]{27} = 3.
$$[/tex]
Next, for the variable part, we use the property of exponents for radicals:
[tex]$$
\sqrt[3]{x^{18}} = x^{\frac{18}{3}} = x^6.
$$[/tex]
Thus, the entire expression simplifies to
[tex]$$
\sqrt[3]{27 x^{18}} = 3 \cdot x^6 = 3 x^6.
$$[/tex]
Therefore, the cube root of [tex]$27x^{18}$[/tex] is [tex]$\boxed{3 x^6}$[/tex].
