3) \( 20 \sqrt{2} \cdot 2 \sqrt{4}^{\frac{1}{4}} \)

First, let's simplify the expression step by step. We know that \( \sqrt{4} = 2 \), so we can rewrite \( 2 \sqrt{4}^{\frac{1}{4}} \) as \( 2 \cdot 2^{\frac{1}{4}} = 2^{1 + \frac{1}{4}} = 2^{\frac{5}{4}} \). Now, rewriting the entire expression: \[ 20 \sqrt{2} \cdot 2^{\frac{5}{4}} = 20 \cdot 2^{\frac{1}{2}} \cdot 2^{\frac{5}{4}} = 20 \cdot 2^{\frac{1}{2} + \frac{5}{4}} = 20 \cdot 2^{\frac{2}{4} + \frac{5}{4}} = 20 \cdot 2^{\frac{7}{4}} \] Next, we simplify further: \[ 20 \cdot 2^{\frac{7}{4}} = 20 \cdot (2^{\frac{3}{4}} \cdot 2^{1.5}) = 20 \cdot 2^{1.5} \] Now, calculating \( 20 \cdot 2^{\frac{7}{4}} = 20 \cdot 2^{1.75} \). To finalize, \( 2^{1.75} = 2^{1.5} \cdot 2^{0.25} = 2 \sqrt{2} \cdot \sqrt{2} = 2^{2} = 4\), thus the complete expression simplifies down to: \[ 20 \cdot 4 = 80 \] So, the final answer is \( 80 \).