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Question
Simplify:
`root(lm)(x^l/x^m)xxroot(mn)(x^m/x^n)xxroot(nl)(x^n/x^l)`
Solution
`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
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