To divide \( \frac{4\sqrt{10}}{\sqrt{2}} \), we can simplify it as follows:
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Rewrite the division: \[ \frac{4\sqrt{10}}{\sqrt{2}} = 4 \cdot \frac{\sqrt{10}}{\sqrt{2}} \]
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Simplify the fraction under the square root: \[ \frac{\sqrt{10}}{\sqrt{2}} = \sqrt{\frac{10}{2}} = \sqrt{5} \]
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Multiply by 4: \[ 4 \cdot \sqrt{5} = 4\sqrt{5} \]
Thus, the exact answer is: \[ \boxed{4\sqrt{5}} \]