Answer
$$2\sqrt[4]{2}w^{\frac{5}{2}}$$
Work Step by Step
Using the rules of radicals to simplify, we find:
$$ \sqrt[4]{8w^3}\sqrt[4]{4w^7}\\ 2\sqrt[4]{2}w^{\frac{3}{4}+\frac{7}{4}}\\ 2\sqrt[4]{2}w^{\frac{5}{2}}$$
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