\((\frac{x^{b}}{x^{c}})^{(b+c-a)}.(\frac{x^{c}}{x^{a}})^{(c+a-b)}.(\frac{x^{a}}{x^{b}})^{(a+b-c)}=?\)
Answer: B
Given exp. = \(x^{(b-c)(b+c-a)}.x^{(c-a)(c+a-b)}.x^{(a-b)(a+b-c)}\)
\(=x^{(b-c)(b+c)-a(b-c)}.x^{(c-a)(c+a)-b(c-a)}.x^{(a-b)(a+b)-c(a-b)}\)
\(= x^{(b^{2}-c^{2}+c^{2}-a^{2}+a^{2}-b^{2})}\)
\(= (x^{0}xx^{0})\)
\(= (1\times1)=1\)