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Find the value of (-(2)/(3))^2/(-(2)/(3)...

Find the value of `(-(2)/(3))^2/(-(2)/(3))^3+((-(4)/(9)))/((2)/(3))^2`

A

`-(1)/(2)`

B

`(3)/(2)`

C

`-(5)/(2)`

D

`(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`(-(2)/(3))^2/(-(2)/(3))^3+((-(4)/(9)))/((2)/(3))^2`
`=(-(2)/(3))^2/((2)/(3))^3-((2)/(3))^(2)/((2)/(3))^2`
`=(1)/((2)/(3))^(3-2)-1 `
`=-(3)/(2)-1=-(5)/(2)`
Hence the correct option is (c).
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