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

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

On simplification [((x)^(ab))/((x)^(a^(2)+b^(2)))]^(a+b)*[((x)^(b^(2)+c^(2)))/((x)^(bc))]^(b+c)*[((x)^(ca))/((x)^(c^(2)+a^(2)))]^(c+) reduces to

On simplification [((x)^(ab))/((x)^(a^(2)+b^(2)))]^(a+b)*[((x)^(b^(2)+c^(2)))/((x)^(bc))]^(b+c)*[((x)^(ca))/((x)^(c^(2)+a^(2)))]^(c+) reduces to

Simplify: (x^(a)/x^(b))^(a+b). (x^(b)/x^(c ))^(b+c) .(x^( c)/x^(a))^(c+a)

(x)/(b)-(a)/(b)+(x)/(a)-(b)/(a)=2

The expression ((x+(1)/(y))^(a)*(x-(1)/(y))^(b))/((y+(1)/(x))^(a)*(y-(1)/(x))^(b)) reduces to a.((x)/(y))^(a-b) b.((y)/(x))^(a-b)backslash c((x)/(y))^(a+b)d.((y)/(x))^(a+b)

(x^a/x^b)^(a+b).(x^b/x^c)^(b+c).(x^c/x^a)^(c+a)