(125)2/3 to radical form?

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Answer 1 · 2018-02-22T15:00:44

$\sqrt[3]{125^{2}}$ $root(3){125^2}$

${(125)}^{\frac{2}{3}}$ $(125)^{2/3}$

$= {(125)}^{2 \cdot \frac{1}{3}}$ $=(125)^{2\cdot 1/3}$

By applying the exponent rule $a^{b \cdot c} = {(a^{b})}^{c}$ $a^{b\cdot c)=(a^b)^c$ , rewrite it as:

$= {(125^{2})}^{\frac{1}{3}}$ $=(125^2)^{1/3}$

Apply the radical rule $a^{1/n}\ =\ root(n){a}$ to get:

$=root(3){125^2}$

That's it!