Question

If `x = a^(m+n),` `y=a^(n+l)` and `z=a^(l+m),` prove that `x^my^nz^l=x^ny^lz^m`

Answer 1

Given `x = a^(m+n),` `y=a^(n+l)` and `z=a^(l+m)`

Putting the values ofx, y and z in `x^my^nz^l,` we get

`x^my^nz^l`

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

`=(a^(m^2+nm))(a^(n^2+ln))(a^(l^2+lm))`

`=a^(m^2+n^2+l^2+nm+ln+lm)`

Putting the values of x, y and z in `x^ny^lz^m,` we get

`x^ny^lz^m`

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

`=(a^(mn+n^2))(a^(nl+l^2))(a^(lm+m^2))`

`=a^(mn+n^2+nl+l^2+lm+m^2)`

So, `x^my^nz^l=x^ny^lz^m`