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Question
Evaluate :
`[ 2^n xx 6^(m + 1 ) xx 10^( m - n ) xx 15^(m + n - 2)]/[4^m xx 3^(2m + n) xx 25^(m - 1)]`
Solution
`[ 2^n xx 6^(m + 1 ) xx 10^( m - n ) xx 15^(m + n - 2)]/[4^m xx 3^(2m + n) xx 25^(m - 1)]`
= `[2^n xx 6^m xx 6 xx 10^m xx 10^(-n) xx 15^m xx 15^n xx 15^(-2 )]/[4^m xx (3^2)^m xx 3^n xx 25^m xx 25^-1 ]`
= `[( 2 xx 1/10 xx 15)^n xx ( 6 xx 10 xx 15 )^m xx 6 xx 1/15^2 ]/[ 3^n xx ( 4 xx 3^2 xx 25 )^m xx 1/25 ]`
= `[ 3^n xx 900^m xx 6/225]/[ 3^n xx 900^m xx 1/25]`
= `6/225 xx 25/1`
= `6/9`
= `2/3`
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