Step-by-step explanation:
[tex] \bf \underline{Solution-} \\ [/tex]
We have to simplify the given expression.
[tex] \rm = \dfrac{ {x}^{a + b} \cdot {x}^{b + c} \cdot {x}^{c + a} }{ {x}^{a} \cdot {x}^{b} \cdot {x}^{c} } [/tex]
We know that:
[tex] \rm \longmapsto {x}^{a} \times {x}^{b} = {x}^{a + b} [/tex]
[tex] \rm \longmapsto \dfrac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} [/tex]
Therefore, we get:
[tex] \rm = \dfrac{ {x}^{(a + b) + (b + c) + (c + a)}}{ {x}^{a + b + c} } [/tex]
[tex] \rm = \dfrac{ {x}^{2(a + b+ c)}}{ {x}^{a + b + c} } [/tex]
[tex] \rm = {x}^{2(a + b+ c) - (a + b + c)}[/tex]
[tex] \rm = {x}^{a + b + c}[/tex]
