QuestionSeptember 19, 2025

8) (2sqrt [5](5p^2))/(sqrt [5](16p))

8) (2sqrt [5](5p^2))/(sqrt [5](16p))
8) (2sqrt [5](5p^2))/(sqrt [5](16p))

Solution
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Answer

\sqrt[5]{10p} Explanation 1. Combine the radicals \frac{2\sqrt[5]{5p^{2}}}{\sqrt[5]{16p}} = 2 \cdot \sqrt[5]{\frac{5p^{2}}{16p}} 2. Simplify inside the radical \frac{5p^{2}}{16p} = \frac{5p}{16}, so expression becomes 2 \cdot \sqrt[5]{\frac{5p}{16}} 3. Separate denominator's 5th root 2 \cdot \frac{\sqrt[5]{5p}}{\sqrt[5]{16}} and \sqrt[5]{16} = 2^{4/5} 4. Simplify coefficient 2 / 2^{4/5} = 2^{1/5}, so we get 2^{1/5}\sqrt[5]{5p} 5. Combine into one radical 2^{1/5}\sqrt[5]{5p} = \sqrt[5]{2 \cdot 5p} = \sqrt[5]{10p}

Explanation

1. Combine the radicals <br /> $\frac{2\sqrt[5]{5p^{2}}}{\sqrt[5]{16p}} = 2 \cdot \sqrt[5]{\frac{5p^{2}}{16p}}$ <br /><br />2. Simplify inside the radical <br /> $\frac{5p^{2}}{16p} = \frac{5p}{16}$, so expression becomes $2 \cdot \sqrt[5]{\frac{5p}{16}}$ <br /><br />3. Separate denominator's 5th root <br /> $2 \cdot \frac{\sqrt[5]{5p}}{\sqrt[5]{16}}$ and $\sqrt[5]{16} = 2^{4/5}$ <br /><br />4. Simplify coefficient <br /> $2 / 2^{4/5} = 2^{1/5}$, so we get $2^{1/5}\sqrt[5]{5p}$ <br /><br />5. Combine into one radical <br /> $2^{1/5}\sqrt[5]{5p} = \sqrt[5]{2 \cdot 5p} = \sqrt[5]{10p}$
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