Question

Simplify:

`root(lm)(x^l/x^m)xxroot(mn)(x^m/x^n)xxroot(nl)(x^n/x^l)`

Answer 1

`root(lm)(x^l/x^m)xxroot(mn)(x^m/x^n)xxroot(nl)(x^n/x^l)`

`=(x^l/x^m)^(1/(lm))xx(x^m/x^n)^(1/(mn))xx(x^n/x^l)^(1/(nl))`

`=(x^(l-m))^(1/ml)xx(x^(m-n))^(1/mn)xx(x^(n-l))^(1/)nl`

`=x^((l-m)/(ml))xx x^((m-n)/(mn))xx x^((n-l)/(nl))`

`=x^((l-m)/(ml)+(m-n)/(mn)+(n-l)/(nl))`

`=x^((ln-mn+lm-nl+nm-lm)/(nml))`

`=x^0`

= 1