Question

(512/729) whole raised to 2/3

Answer 1

(512/729)^2/3

8^3=512 & 9^3=729

Therefore, 512/729 can be expressed as (8^3/9^3)^2/3

= (8/9)^3*2/3

=(8/9)^2

=64/81

Answer = 64/81

Answer 2

$\bf \underline{Solution-}$

$\textsf{Given,}$

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

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

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

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

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

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

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

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