Question

expand
$\sqrt[3]{3}$
in increasing power of 2/3​

Answer 1

$Value \: of \: \big( \sqrt[3]{3}\big)^{\frac{2}{3}}$

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

$= 3^{\big(\frac{1}{3} \times \frac{2}{3}\big) }$

$= 3^{\frac{2}{9}}$

$= \sqrt[9]{3^{2}}$

$= \sqrt[9]{9}$

Therefore.,

$\red {Value \: of \: \big( \sqrt[3]{3}}\big)^{\frac{2}{3}}$

$\green{ = \sqrt[9]{9} }$

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