Question

find the value of ( 729/512 )-⅔​

Answer 1

Answer:

$= > \frac{64}{81}$

Step-by-step explanation:

$= > { (\frac{729}{512}) }^{ - \frac{2}{3} } \\ \\ = > { (\frac{729}{512} )}^{ \frac{1}{3} \times - 2} \\ \\ = > {( \frac{ \sqrt[3]{729} }{ \sqrt[3]{512} } )}^{ - 2} \\ \\ = > { (\frac{9}{8} )}^{ - 2} \\ \\ = > { (\frac{8}{9} )}^{2} \\ \\ = > \frac{64}{81}$

Answer 2

Step-by-step explanation:

$\bf \underline{Solution-}$

$\textsf{Given,}$

$\sf{ \bigg( \frac{729}{512} \bigg) ^{ - \frac{2}{3} } }$

$\sf{ \Rightarrow \: \frac{1}{(729 {)}^{ \frac{2}{3} } } \times (512 {)}^{ \frac{2}{3} } }$

$\sf{ \Rightarrow \: \frac{(512 {)}^{ \frac{2}{3} } }{(729 {)}^{ \frac{2}{3} } } }$

$\sf{ \Rightarrow \: \frac{( {8}^{3} {)}^{ \frac{2}{3} } }{( {9}^{3} {)}^{ \frac{2}{3} } } }$

$\sf{ \Rightarrow \: \frac{ {8}^{ \cancel{3} \times \frac{2}{ \cancel{3}} } }{{9}^{ \cancel{3} \times \frac{2}{ \cancel{3}}}} }$

$\sf{ \Rightarrow \: \frac{ {8}^{2}}{{9}^{2} }}$

$\sf{ \Rightarrow \: \frac{8 \times 8}{9 \times 9} }$

$\sf{ \Rightarrow \: \frac{64}{81} \: \: \bf{Ans.} }$