# How do you simplify (216/729)^(2/3)?

Sep 1, 2016

$\frac{4}{9}$

#### Explanation:

It is a real advantage to know all the powers up to 1000 by heart.

We would then know at once that $\text{ } 216 = {6}^{3} \mathmr{and} 729 = {9}^{3}$

Else you have to find the prime factors first.

An index that is a fraction shows both a root and a power.

${x}^{\frac{p}{q}} = \sqrt[q]{{x}^{p}} = {\left(\sqrt[q]{x}\right)}^{p}$

${\left(\frac{216}{729}\right)}^{\frac{2}{3}} = {\left(\sqrt[3]{\frac{216}{729}}\right)}^{2}$

=${\left(\frac{6}{9}\right)}^{2} \text{ = } {\left(\frac{2}{3}\right)}^{2}$

=$\frac{4}{9}$