Question

(\frac{3sqrt{6}}{2sqrt{27}})

Explanation:

Step1: Simplify the cube roots

First, we simplify the cube roots. Recall that $\sqrt[3]{27} = 3$ because $3^3 = 27$, and $\sqrt[3]{6}$ remains as is since 6 is not a perfect cube. So the expression becomes $\frac{3\sqrt[3]{6}}{2\times3}$.

Step2: Cancel out the common factor

Now, we can cancel out the common factor of 3 in the numerator and the denominator. The 3 in the numerator and the 3 in the denominator (from $2\times3$) will cancel each other, leaving us with $\frac{\sqrt[3]{6}}{2}$.

Answer:

$\frac{\sqrt[3]{6}}{2}$