# How do you simplify 125^(2/3)?

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44
Feb 25, 2017

=color(blue)(25

#### Explanation:

125^(2/3

$125 = 5 \times 5 \times 5$

$125 = {5}^{3}$

125^(2/3) = 5^(3 (2/3)

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Consider just the indices:
$3 \times \frac{2}{3} = \frac{{\cancel{3}}^{1} \times 2}{{\cancel{3}}^{1}} = 2$
..............................................................................

$= {5}^{2}$

=color(blue)(25

Then teach the underlying concepts
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#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

12
Apr 5, 2017

$\textcolor{red}{25}$

#### Explanation:

${125}^{\frac{2}{3}}$

$\therefore = \sqrt[3]{{125}^{2}}$

$\therefore = \sqrt[3]{15625}$

$\therefore = \sqrt[3]{25 \cdot 25 \cdot 25}$

:.color(red)(=root3(a) xx root3(a) xx root3(a)=a

:.color(red)(=25

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