Question

The value of: [(27)^2/3 × (8)^2/3]/9^3/2 is
(a) 1/3
(b) 2/3
(c) 3/3
(d) 4/3​

Answer 1

Explanation:

➤ Given:-

`\sf{\frac{(27 {)}^{ (2)/(3) } * (8 {)}^{ (2)/(3) } }{(9 {)}^{ (3)/(2) } } } \\`

➤ To find:-

• 
  `{\sf Simplifyed \:form = ?}\\`

➤ Solution:-

`\textsf{We have,}\\`

`\sf{\frac{(27 {)}^{ (2)/(3) } * (8 {)}^{ (2)/(3) } }{(9 {)}^{ (3)/(2) } } } \\`

`\sf \leadsto \: {\frac{( {3}^(3) {)}^{ (2)/(3) } * ( { {2}^(3) )}^{ (2)/(3) } }{( {3}^(2) {)}^{ (3)/(2) } } } \\`

`\sf \leadsto \: \frac{ {3}^{ \cancel3 * (2)/( \cancel3) } * {2}^{ \cancel3 * (2)/( \cancel3) } }{ {3}^{ \cancel2 * (3)/( \cancel2) } } \\`

`\sf \leadsto \: \frac{ {3}^(2) * {2}^(2) }{(3 {)}^(3) } \\`

`\sf \leadsto \: \frac{ {2}^(2) }{ {3}^((3 - 2))} \\`

`\sf \leadsto \: \frac{ {2}^(2) } { {3}^(1) } \\`

`\sf \leadsto \: (2 * 2)/(3) \\`

`\sf \leadsto \: (4)/(3) \\`