Solve: Square Root of 4 Divided by Cube Root of 4

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

• Step 1: Convert the roots to exponent notation
• Step 2: Apply the quotient of powers rule
• Step 3: Simplify the expression

Now, let's work through each step:
Step 1: Convert the roots to exponent notation:
$\sqrt{4} = 4^{1/2}$ and $\sqrt[3]{4} = 4^{1/3}$.
Step 2: Calculate the quotient using the rule $\frac{a^m}{a^n} = a^{m-n}$:

$\frac{4^{1/2}}{4^{1/3}} = 4^{(1/2) - (1/3)}$

Step 3: Simplify the exponent:

$1/2 - 1/3 = \frac{3}{6} - \frac{2}{6} = \frac{1}{6}$

Therefore, the expression simplifies to:

$4^{\frac{1}{6}}$

The correct answer is choice 1: $4^{\frac{1}{6}}$.