Question

Evaluate : 
`3^3 xx ( 243 )^(-2/3) xx 9^(-1/3)`

Answer 1

`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`