which expression is equivalent to $sqrt3{216x^{27}}$?\n$6x^{3}$\n$6x^{9}$\n$72x^{3}$\n$72x^{9}$

Explanation:

Step1: Find cube - root of 216

We know that $6\times6\times6 = 216$, so $\sqrt[3]{216}=6$.

Step2: Find cube - root of $x^{27}$

Using the rule $\sqrt[n]{a^{m}}=a^{\frac{m}{n}}$, for $n = 3$ and $m = 27$, we have $\sqrt[3]{x^{27}}=x^{\frac{27}{3}}=x^{9}$.

Step3: Combine the results

$\sqrt[3]{216x^{27}}=\sqrt[3]{216}\times\sqrt[3]{x^{27}} = 6x^{9}$.

Answer:

B. $6x^{9}$