Solve: Cube Root of 6 Divided by Square Root of 6

To solve this problem, we'll follow these steps:

• Step 1: Convert the given radical expressions into their equivalent fractional power forms.
• Step 2: Use the properties of exponents to simplify the expression.
• Step 3: Convert the result back into a radical form if necessary.

Let's execute these steps:
Step 1: Write $\sqrt[3]{6}$ and $\sqrt{6}$ in terms of fractional powers:
$\sqrt[3]{6} = 6^{1/3}$ and $\sqrt{6} = 6^{1/2}$.

Step 2: Apply the quotient rule for exponents:
$\frac{6^{1/3}}{6^{1/2}} = 6^{1/3 - 1/2} = 6^{\frac{1}{3} - \frac{1}{2}} = 6^{\frac{2 - 3}{6}} = 6^{-\frac{1}{6}}$.

Step 3: Simplify and express back in radical form:
Since a negative exponent denotes the reciprocal, we have $6^{-\frac{1}{6}}$ = $\frac{1}{6^{\frac{1}{6}}}$, which simplifies to $\sqrt[6]{6}$.

Therefore, the expression simplifies to $\sqrt[6]{6}$.

Thus, the solution to the problem is $\sqrt[6]{6}$, which corresponds to choice 3.