`[{(x^(a(a-b)))/(x^(a(a+b)))}-:{(x^(b(b-a)))/(x^(b(b+a)))}]^(a+b)=1`

On simplification [(x^((a)/(a-b)))/(x^((a)/(a+b)))-:(x^((b)/(b-a)))/(x^((b)/(b+a)))]^(a+b) reduces to

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

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

Prove that: ((x^(a))/(x^(b)))^(c)x((x^(b))/(x^(c)))^(a)x((x^(c))/(x^(a)))^(b)=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

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))

(1)/(1+x^(a-b)+x^(a-c))+(1)/(1+x^(b-c)+x^(b-a))+(1)/(1+x^(c-a)+x^(c-b))

((x^(a))/(x^(b)))^(a+b)*((x^(b))/(x^(c)))^(b+c)*((x^(c))/(x^(a)))^(c+a)=? a.0 b.x^(abc) c.x^(a+b+c)d.1=? a.0

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