JEE Novice - (33)

$\Large \left(\dfrac{x^a}{x^b}\right)^{a^2+ab+b^2} . \left(\dfrac{x^b}{x^c}\right)^{b^2+bc+c^2} . \left(\dfrac{x^c}{x^a}\right)^{c^2+ca+a^2}$ $\Large = { x }^{ \left( a-b \right) \left( { a }^{ 2 }+ab+{ b }^{ 2 } \right) }.{ x }^{ \left( b-c \right) \left( { b }^{ 2 }+bc+{ c }^{ 2 } \right) }.{ x }^{ \left( c-a \right) \left( { c }^{ 2 }+ac+{ a }^{ 2 } \right) }$ $\Large = { x }^{ { a }^{ 3 }-{ b }^{ 3 } }.{ x }^{ { b }^{ 3 }-{ c }^{ 3 } }.{ x }^{ { c }^{ 3 }-{ a }^{ 3 } }$ $\Large = { x }^{ { a }^{ 3 }-{ b }^{ 3 }+{ b }^{ 3 }-{ c }^{ 3 }+{ c }^{ 3 }-{ a }^{ 3 } }$ $\Large = { x }^{ 0 }$ $\Huge =\boxed { 1 }$