Question

Find the exact value of n in 9⅓ ×27^n = 27⅘ and express it in fraction . Its urgent​

Answer 1

n = 26/45

Explanation:

If the 9⅓ and 27⅘ are supposed to be
`9^(1/3)` and
`27^(4/5)`, then

`9^(1/3)` ×
`27^(n)` =
`27^(4/5)`

=>
`(3^(2))^(1/3)` ×
`(3^3)^(n)` =
`(3^3)^(4/5)`

=>
`3^(2/3)` ×
`3^(3n)` =
`3^(12/5)`

=>
`3^{3n+(2)/(3)}` =
`3^(12/5)`

=> 3n+2/3 = 12/5

=> 45n + 10 = 36

=> 45n = 26

=> n = 26/45