which expression is equivalent to $sqrt3{27x^{18}}$?\n$3x^{3}$\n$3x^{6}$\n$9x^{3}$\n$9x^{6}$

Explanation:

Step1: Simplify cube - root of 27

The cube - root of 27 is 3 since $3^3=27$, i.e., $\sqrt[3]{27}=3$.

Step2: Simplify cube - root of $x^{18}$

Using the rule $\sqrt[n]{a^m}=a^{\frac{m}{n}}$, for $\sqrt[3]{x^{18}}$, we have $x^{\frac{18}{3}} = x^6$.

Step3: Combine the results

$\sqrt[3]{27x^{18}}=\sqrt[3]{27}\times\sqrt[3]{x^{18}} = 3x^6$.

Answer:

B. $3x^6$