Question

Simplify
$( \frac{3125}{243} {)}^{ \frac{ -4}{3} }$
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Answer 1

$( \frac{3125}{243} ) ^{ - \frac{4}{3} } \\ \\ \\ =>( \frac{243}{3125} ) ^{ \frac{4}{3} } \\ \\ \\ = > \sqrt[3]{ ({ \frac{243}{3125} } } ) ^{4} \\ \\ \\ => \sqrt[3]{ \frac{243}{3125} \times \frac{243}{3125} \times \frac{243}{3125} \times \frac{243}{3125} } \\ \\ \\ => \frac{243}{3125} \times \frac{ \sqrt[3]{243}} {\sqrt[3]{3125}} \\ \\ \\ => \frac{243} {3125} \times \frac{3 \sqrt[3]{9} }{5 \sqrt[3]{25} } \\ \\ \\ = > \frac{729 \sqrt[3]{9} }{15625 \sqrt[3]{25} } \\ \\ \\ \mathbf{ By \: Rationalization, } \\ \\ \\ = > \frac{729 \sqrt[3]{9 \times 25} }{15625 \times 25} \\ \\ \\ = > \frac{729 \sqrt[3]{225} }{390625}$