Evaluate each of the following: `(i) (2/(11))^4 xx ((11)/3)^2 xx (3/2)^3` `(ii)\ (1/2)^5 xx ((-2)/3)^4xx (3/5)^(-1)`

Explanation

Solutions:
Given,
`(i) (2/(11))^4 xx ((11)/3)^2 xx (3/2)^3`
using
`=(a/b)^m=(a)^m/(b)^m`
`=>(2^4)/(11^4) xx (11^2)/(3^2) xx (3^3)/(2^3)`
By cancelling, we get
`=>(2^1)/(11^2) xx (3^1)`
`=6/121`
Given
`(ii) (1/2)^5 xx ((-2)/3)^4xx (3/5)^(-1)`
Using
=`(ab)^-n = (b/a)^n`
`(1^5)/(2^5) xx (-2^4)/(3^4) xx (3^-1)/(5^-1)`
`(1^5)/(2^5) xx (2^4) - (-1^4)/(3^4) xx 5/3`
By cancelling we get
`1/2 xx 1/3^4 xx 5/3`
`= 5/ 2 xx 3^4 xx3`
`= 5/2 xx 3^3 xx 3^3 xx 3`
`=5/2 xx 9 xx 9 xx 3`
`= 5/486`
Hence the required answers are `6/121` and`5/486`.