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Question
Evaluate :
`3^3 xx ( 243 )^(-2/3) xx 9^(-1/3)`
Solution
`3^3 xx ( 243 )^(-2/3) xx 9^(1/3)`
= `3^3 xx ( 3 xx 3 xx 3 xx 3 xx 3 )^( - 2/3 ) xx ( 3 xx 3 )^( -1/3 )`
= `3^3 xx ( 3^5 )^( - 2/3 ) xx ( 3^2 )^(1/3)`
= `3^3 xx 3^( - 10/3 ) xx 3^( -2/3 ) ...[( a^m )^n = a^( mn )]`
= `3^( 3 - 10/3 - 2/3 ) [ a^m xx a^n xx a^o = a^( m + n + o )]`
=`3^([ 9 - 10 - 2]/3)`
= `3^( [9 - 12]/3 )`
= `3^( - 3/3 )`
= `3^-1`
= `1/3`
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