Show that: `(i)\ (x^(a-b))^(a+b)\ (x^(b-c))^(b+c)\ (x^(c-a))^(c+a)=1` `(ii)\ {(x^a-a^((-1)))^(1/(a-1))}^(a/(a+1))=x`

Show that: (x^(a-b))^(a+b)(x^(b-c))^(b+c)(x^(c-a))^(c+a)=1{(x^(a)-a^((-1)))^((1)/(a-1))}^((a)/(a+1))=x

Show that (x^(a+b))^(a-b)times(x^(b+c))^(b-c)times(x^(c+a))^(c-a)=1

Show that: (i) (x^(a(b-c)))/(x^(b(a-c)))-:((x^b)/(x^a))^c=1,

Show that : (i) x^(a(b-c))/(x^(b(a-c)))/((x^b)/(x^a))^c=1 , (ii) ((x^(a+b))^2(x^(b+c))^2(x^(c+a))^2)/((x^a x^b x^c)^4)=1

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))

Show that: (x^(a(b-c)))/(x^(b(a-c)))-:((x^(b))/(x^(a)))^(c)=1((x^(a+b))(x^(b+c))^(2)(x^(c+a))^(2))/((x^(a)x^(b)x^(c))^(4))=1

Show that : (x^(a(b-c)))/(x^(b(a-c)))*(x^(b))/(x^(a)))^(c)=1((x^(a+b))^(2)(x^(b+c))(x^(c+a))^(2))/((x^(a)x^(b)x^(c))^(4))=1

Show that: 1/(1+x^(b-a)+x^(c-a))+1/(1+x^(a-b)+\ x^(c-b))+1/(1+x^(b-c)+\ x^(a-c))=1

(x^(b)/(x^(c)))^(a)xx(x^(c)/(x^(a)))^(b)xx(x^(a)/(x^(b)))^(c)=1

Prove that. (i) sqrt(x^(-1) y) .sqrt(y^(-1) z) . Sqrt(z^(-1) x) = 1 (ii) ((1)/(x^(a-b)))^((1)/(a-c)).((1)/(x^(b-c))).((1)/(x^(c-b)))^((1)/(c-b))= 1 (iii) (x^(a(b-c)))/(x^(b(a-c))) div ((x^(b))/(x^(a))) (iv) ((x^(a+b))^(2)(x^(b+c))^(2)(x^(c+a))^(2))/((x^(a)x^(b)x^(c))^(4))