What is $625^{\frac{1}{8}}$ $625^(1/8)$ in radical form?

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What is $625^{\frac{1}{8}}$ $625^(1/8)$ in radical form?

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Answer 1 · 2017-05-01T03:43:36

$\sqrt[8]{625} = \sqrt{5}$ $root(8)(625) = sqrt(5)$

Explanation:

Use the exponent rules $\sqrt{x} = x^{\frac{1}{2}}$ $sqrt(x) = x^(1/2)$ ; $\sqrt[3]{y} = y^{\frac{1}{3}}$ $" "root(3)(y) = y^(1/3)$

and the exponent power rule ${(x^{m})}^{n} = x^{m \cdot n}$ $(x^m)^n = x^(m*n)$

$625^{\frac{1}{8}} = \sqrt[8]{625}$ $625^(1/8) = root(8)(625)$

Simplified: $625^{\frac{1}{8}} = {(625^{\frac{1}{2}})}^{\frac{1}{4}} = {({(625^{\frac{1}{2}})}^{\frac{1}{2}})}^{\frac{1}{2}}$ $625^(1/8) = (625^(1/2))^(1/4) = ((625^(1/2))^(1/2))^(1/2)$

$625^{\frac{1}{8}} = \sqrt{\sqrt{\sqrt{625}}} = \sqrt{\sqrt{25}} = \sqrt{5}$ $625^(1/8) = sqrt(sqrt(sqrt(625))) = sqrt(sqrt(25)) = sqrt(5)$

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What is $625^{\frac{1}{8}}$ $625^(1/8)$ in radical form?

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