Question

How to solve this?

If

`a=x^(m+n) * y^l`

`b=x^(n+l) * y^m`

`c=x^(l+m) * y^n`

prove that `a^(m-n) * b^(n-l) * c^(l-m)=1`

Answer 1

`a^(m-n)b^(n-l)c^(l-m)`
`=(x^(m+n)y^l)^(m-n)(x^(n+l)y^m)^(n-l)(x^(l+m)y^n)^(l-m)`
`=x^((m+n)(m-n)+(n+l)(n-l)+(l+m)(l-m) times`
`y^(l(m-n)+m(n-l)+n(l-m))`
`=x^(m^2-n^2+n^2-l^2+l^2-m^2)y^(lm-ln+mn-ml+nl-nm)`
`=x^0y^0=1`