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Question
Evaluate:
`( 27/125 )^(2/3) xx ( 9/25 )^(-3/2)`
Solution
`( 27/125 )^(2/3) xx ( 9/25 )^(-3/2)`
= `([ 3 xx 3 xx 3 ]/[ 5xx 5 xx 5 ])^(2/3) xx ([ 3 xx 3 ]/[ 5 xx 5 ])^( -3/2 )`
= `[(3/5)^3 ]^(2/3) xx [(3/5)^2]^(-3/2)`
= `(3/5)^( 3 xx 2/3 ) xx (3/5)^( 2 xx - 3/2)`
= `(3/5)^2 xx (3/5)^(-3)`
= `(3/5)^( 2 - 3 )`
= `(3/5)^( -1 )`
= `1/(3/5)`
`= 5/3`
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