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)`

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

If x^(a)=c^(b) and x^(c )=c^(a) show that a^(2)=bc

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

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

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

a(y+z)=x,b(z+x)=y,c(x+y)=z prove that (x^(2))/(a(1-bc))=(y^(2))/(b(1-ca))=(z^(2))/(c(1-ab))

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

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

The value of ((x^(a))/(x^(b)))^((1)/(ab)) xx ((x^(b))/(x^(c)))^((1)/(bc)) xx ((x^(c))/(x^(a)))^((1)/(ca)) is equal to