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How do you write $5^{\frac{2}{3}}$ $5^(2/3)$ in radical form?

1 Answer

Mar 14, 2017

$5^{\frac{2}{3}} = \sqrt[3]{5^{2}}$ $5^(2/3) = color(green)(root(3)(5^2)$ or $\sqrt[3]{25}$ $color(green)(root(3)25)$

Explanation:

In general:
$XXX c^{\frac{1}{b}}$ $color(white)("XXX")c^(1/b)$ means $\sqrt[b]{c}$ $root(b)(c)$
and
$XXX c^{\frac{a}{b}}$ $color(white)("XXX")c^(a/b)$ means ${(\sqrt[b]{c})}^{a}$ $(root(b)(c))^a$ or (equivalently) $\sqrt[b]{c^{a}}$ $root(b)(c^a)$

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