Question

Show that :
`( a^m/a^-n)^( m - n ) xx (a^n/a^-l)^( n - l) xx (a^l/a^-m)^( l - m ) = 1`

Answer 1

`( a^m/a^-n)^( m - n ) xx (a^n/a^-l)^( n - l) xx (a^l/a^-m)^( l - m ) = 1`

= `( a^m xx a^n )^( m - n ) xx ( a^n xx a^l )^( n - l ) xx ( a^l xx a^m )^( l - m )`

= `( a^(m + n))^( m - n ) xx ( a^( n + l ))^( n - l ) xx ( a^( l + m ))^( l - m )`

= `a^( m^2 - n^2 ) xx a^( n^2 - l^2 ) xx a^( l^2 - m^2 )`

= `a^( m^2 - n^2 + n^2 - l^2 + l^2 - m^2 )`

= `a^0`
= 1