Simplify:
`(i)\ ((x^(a+b))/(x^c))^(a-b)\ ((x^(b+c))/(x^a))^(b-c)\ ((x^(c+a))/(x^b))^(c-a)`
`(ii)\ ((x^l)/(x^m))^(1/(lm))\ xx\ ((x^m)/(x^n))^(1/(mn))\ xx\ \ ((x^n)/(x^l))^(1/(ln))`

Explanation

(i) `=((x^(a + b))/(x^c))^(a-b)xx((x^(b+c))/(x^a))^(b - c)xx((x^(c+a))/(x^b))^(c-a)`
`=(x^((a+b)(a-b)))/(x^ (c(a-b)))xx(x^((b+c)(b-c)))/(x^( a(b-c)))xx(x^((c+a)(c-a)))/(x^ (b(c-a)))`
`=(x^((a+b)(a-b)))/(x^(ca-bc))xx(x^((b+c)(b-c)))/(x^(ab-ac))(x^((c+a)(c-a)))/(x^(bc-ab))`
`=(x^(a^2-b^2)x^(b^2-c^2)x^(c^2-a^2))/(x^(ca-bc+ab-ac+bc-a^c))`
`=(x^(a^2-b^2+b^2-c^2+c^2-a^2))/(x^(ca-bc+ab-ac+bc-ab))`
`=x^0x^0`
`=1`

(ii)`=(x^l/x^m )^(1/(lm))*(x^m/x^n)^(1/(mn))*(x^n/x^l )^(1/(nl))`
`=(x^(l-m))^((1/(lm)))*(x^(m-n))^((1/(mn)))*(x^(n-l))^((1/(nl)))`
`=x^((l-m)/(lm))*x^((m-n)/(mn))*x^((n-l)/(nl))`
`=x^((l-m)/(lm)+(m-n)/(mn)+(n-l)/(nl))`
`=x^ 0=1`