[tex]\sf\left(\dfrac{x^{a^2+b^2}}{x^{ab}}\right)^{a+b}\left(\dfrac{x^{b^2+c^2}}{x^{bc}}\right)^{b+c}\left(\dfrac{x^{c^2+a^2}}{x^{ca}}\right)^{c+a} \\ = {x}^{ ({a}^{2} + {b}^{2} - ab)(a + b)} \: \: {x}^{ ({b}^{2} + {c}^{2} - bc)( b + c)} \: \: {x}^{ ({c}^{2} + {a}^{2} - ca)(c + a)} \\ = {x}^{ {a}^{3} + {b}^{3 } - {a}^{2}b + {a}^{2} b + {b}^{3} - a {b}^{2} } \: \: {x}^{ {b}^{3} + {c}^{3 } - {b}^{2}c + {b}^{2} c + {c}^{3} - b{c}^{2} } \: \: {x}^{ {c}^{3} + {a}^{3 } - {c}^{2}a + {c}^{2} a + {c}^{3} - c {a}^{2} } \: \: \\ = {x}^{{a}^{3} + {b}^{3 } - {a}^{2}b + {a}^{2} b + {b}^{3} - a {b}^{2} + {b}^{3} + {c}^{3 } - {b}^{2}c + {b}^{2} c + {c}^{3} - b{c}^{2} + {c}^{3} + {a}^{3 } - {c}^{2}a + {c}^{2} a + {c}^{3} - c {a}^{2}} \\
= {x}^{ {a}^{3} + {b}^{3} } \: \: {x}^{ {b}^{3} + {c}^{3} } \: \: {x}^{ {c}^{3} + {a}^{3} } \\ = {x}^{{a}^{3} + {b}^{3} + {b}^{3} + {c}^{3} + {c}^{3} + {a}^{3}}
\\ = {x}^{2 {a}^{3} + 2 {b}^{3} + 2 {c}^{3} } \\ = {x}^{2( {a}^{3} + {b}^{3} + {c}^{3} } [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
