Question 1041672
{{{(x^(1/(a-b)))^(1/(a-c))*(x^(1/(b-c)))^(1/(b-a))*(x^(1/(c-a)))^(1/(c-b))}}}


={{{x^(1/((a-b)(a-c)))*x^(1/((b-c)(b-a)))*x^(1/((c-a)(c-b)))}}}


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


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


={{{x^((b-c-a+c+a-b )/((a-b)(a-c)(b-c))) = x^0 = 1}}}