The value of $${\left( {{x^{b + c}}} \right)^{b - c}}$$   $$ \times $$ $${\left( {{x^{c + a}}} \right)^{c - a}}$$   $$ \times $$ $${\left( {{x^{a + b}}} \right)^{a - b}}$$   is?

Solution (By Examveda Team)

$$\eqalign{ & {\left( {{x^{b + c}}} \right)^{b - c}} \times {\left( {{x^{c + a}}} \right)^{c - a}} \times {\left( {{x^{a + b}}} \right)^{a - b}}\left( {x \ne 0} \right) \cr & = {x^{{b^2} - {c^2}}} \times {x^{{c^2} - {a^2}}} \times {x^{{a^2} - {b^2}}} \cr & = {x^{{b^2} - {c^2} + {c^2} - {a^2} + {a^2} - {b^2}}} \cr & = {x^0} \cr & = 1 \cr} $$