Simplify the Expression: (√8/2√16) × (√64/√2√4)

To solve this problem, we'll simplify the expression step-by-step:

Step 1: Simplify each root expression:
- $\sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}$
- $\sqrt{16} = 4$
- $\sqrt{64} = 8$
- $\sqrt{2} = \sqrt{2}$
- $\sqrt{4} = 2$

Step 2: Substitute back into the original expression:
$\frac{\sqrt{8}}{2 \cdot \sqrt{16}} = \frac{2\sqrt{2}}{2 \cdot 4} = \frac{\sqrt{2}}{4}$

$\frac{\sqrt{64}}{\sqrt{2} \cdot \sqrt{4}} = \frac{8}{\sqrt{2} \cdot 2} = \frac{8}{2\sqrt{2}} = \frac{4}{\sqrt{2}}$

Step 3: Multiply the simplified fractions:
$\frac{\sqrt{2}}{4} \cdot \frac{4}{\sqrt{2}} = \frac{\sqrt{2} \cdot 4}{4 \cdot \sqrt{2}} = \frac{4\sqrt{2}}{4\sqrt{2}} = 1$

Therefore, the solution to the problem is $1$.