b) \( \frac{\sqrt[4]{4} \cdot \sqrt{\sqrt{9}}}{\sqrt{6}}= \)
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To solve \( \frac{\sqrt[4]{4} \cdot \sqrt{\sqrt{9}}}{\sqrt{6}} \), let’s break it down step by step. First, simplify \( \sqrt[4]{4} \): \[ \sqrt[4]{4} = \sqrt[4]{2^2} = 2^{1/2} = \sqrt{2} \] Next, simplify \( \sqrt{\sqrt{9}} \): \[ \sqrt{9} = 3 \quad \text{so} \quad \sqrt{\sqrt{9}} = \sqrt{3} \] Thus, we can rewrite the expression: \[ \frac{\sqrt{2} \cdot \sqrt{3}}{\sqrt{6}} \] Now, note that \( \sqrt{6} = \sqrt{2 \cdot 3} = \sqrt{2} \cdot \sqrt{3} \). Therefore, the expression simplifies to: \[ \frac{\sqrt{2} \cdot \sqrt{3}}{\sqrt{2} \cdot \sqrt{3}} = 1 \] So, \( \frac{\sqrt[4]{4} \cdot \sqrt{\sqrt{9}}}{\sqrt{6}} = 1 \). The final answer is: \[ \boxed{1} \]