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Step-by-step explanation:
[tex] \sf{\frac{(27 {)}^{ \frac{2}{3} } \times (8 {)}^{ \frac{2}{3} } }{(9 {)}^{ \frac{3}{2} } } } \\ [/tex]
[tex]\textsf{We have,}\\[/tex]
[tex]\sf{\frac{(27 {)}^{ \frac{2}{3} } \times (8 {)}^{ \frac{2}{3} } }{(9 {)}^{ \frac{3}{2} } } } \\ [/tex]
[tex]\sf \leadsto \: {\frac{( {3}^{3} {)}^{ \frac{2}{3} } \times ( { {2}^{3} )}^{ \frac{2}{3} } }{( {3}^{2} {)}^{ \frac{3}{2} } } } \\ [/tex]
[tex]\sf \leadsto \: \frac{ {3}^{ \cancel3 \times \frac{2}{ \cancel3} } \times {2}^{ \cancel3 \times \frac{2}{ \cancel3} } }{ {3}^{ \cancel2 \times \frac{3}{ \cancel2} } } \\ [/tex]
[tex]\sf \leadsto \: \frac{ {3}^{2} \times {2}^{2} }{(3 {)}^{3} } \\ [/tex]
[tex]\sf \leadsto \: \frac{ {2}^{2} }{ {3}^{(3 - 2)}} \\ [/tex]
[tex]\sf \leadsto \: \frac{ {2}^{2} } { {3}^{1} } \\ [/tex]
[tex]\sf \leadsto \: \frac{2 \times 2}{3} \\ [/tex]
[tex]\sf \leadsto \: \frac{4}{3} \\ [/tex]