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

Answer: Option B

$$\begin{array}{rl}& \text{Given Exp}\text{.}\\ & =x^{\left(b-c\right)\left(b+c-a\right)}.x^{\left(c-a\right)\left(c+a-b\right)}.x^{\left(a-b\right)\left(a+b-c\right)}\end{array}$$
  $$=x^{\left(b-c\right)\left(b+c\right)-a\left(b-c\right)}.$$    $$x^{\left(c-a\right)\left(c+a\right)-b\left(c-a\right)}.$$   $$x^{\left(a-b\right)\left(a+b\right)-c\left(a-b\right)}$$
\begin{aligned} & = {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)}} \\ & = {{x^0} . {x^\left( -ab + ac - bc + ba - ca + cb \right)}} \\ & = \left( {{x^0} \times {x^0}} \right) \\ & = \left( {1 \times 1} \right) \\ & = 1 \\\end{aligned}