( x^bx^c )^ ( b + c - a ). ( x^cx^a )^ ( c + a - b ). ( x^ax^b )^ ( a + b - c ) = ?

Answer: Option B

$$x^{\left(b-c\right)\left(b+c-a\right)}.x^{\left(c-a\right)\left(c+a-b\right)}.x^{\left(a-b\right)\left(a+b-c\right)}$$
  $$=x^{\left(b-c\right)\left(b+c\right)-a\left(b-c\right)}.$$    $$x^{\left(c-a\right)\left(c+a\right)-b\left(c-a\right)}.$$   $$x^{\left(a-b\right)\left(a+b\right)-c\left(a-b\right)}$$
$$\begin{array}{rl}& =x^{\left(b^2-c^2+c^2-a^2+a^2-b^2\right)}.x^{-a\left(b-c\right)-b\left(c-a\right)-c\left(a-b\right)}\\ & =\left(x^0\times x^0\right)\\ & =\left(1\times 1\right)\\ & =1\end{array}$$