If a+b+c =0 Prove that `root(bc)(x^(a^(2))/x^(bc))xxroot(ca)(x^(b^(2))/x^(ca))xxroot(ab)(x^(c^(2))/x^(ab))=1`

Show that (x^(b-c))^((1)/(bc))xx(x^(c-a))^((1)/(ca))xx(x^(a-b))^((1)/(ab))=1 .

(x^(b)/x^(c ))^(1/(bc))xx(x^(c )/x^(a))^(1/(ca))xx(x^(a)/x^(b))^(1/(ab))

Prove that x^((b-c)/(bc)) x^((c-a)/(ca)) x^((a-b)/(ab))=1

If a + b + c = 0, then x^((a^(2))/(bc)), x^((b^(2))/(ca)) , x((c^(2))/(ab)) equals :

Prove that: ((x^(a))/(x^(b)))^(a)-2+ab+b^(2)x((x6b)/(x^(c)))^(b)-2+bc+c^(2)x((x^(c))/(x^(a)))^(c)-2+ca+a^(2)

If x^(a).x^(b).x^(c )=1 (x ne 0) show that x^(a^(2)/(bc)).x^(b^(2)/(ca)).x^(c^(2)/(ab))=x^(3)

If a+b+c=0, then the value of (x^(a))^(a^(2)-bc)*(x^(b))^(b^(2)-ca)*(x^(c))^(c^(2)-ab) is equal to a 0 b.1 c.-1 d.-2

For any positive real number x;write the value of {(x^(a))^(b)}^((1)/(ab)){(x^(b))^(c)}^((1)/(bc)){(x^(c))^(a)}^((1)/(ca))