Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[{x}^{(a+b)(a-b)}{({x}^{b+c})}^{b-c}{({x}^{c+a})}^{c-a}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[{x}^{(a+b)(a-b)}{x}^{(b+c)(b-c)}{({x}^{c+a})}^{c-a}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[{x}^{(a+b)(a-b)}{x}^{(b+c)(b-c)}{x}^{(c+a)(c-a)}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[{x}^{(a+b)(a-b)+(b+c)(b-c)+(c+a)(c-a)}\]
Expand.
\[{x}^{{a}^{2}-{b}^{2}+{b}^{2}-{c}^{2}+{c}^{2}-{a}^{2}}\]
Collect like terms.
\[{x}^{({a}^{2}-{a}^{2})+(-{b}^{2}+{b}^{2})+(-{c}^{2}+{c}^{2})}\]
Simplify \(({a}^{2}-{a}^{2})+(-{b}^{2}+{b}^{2})+(-{c}^{2}+{c}^{2})\) to \(0\).
\[{x}^{0}\]
Use Rule of Zero: \({x}^{0}=1\).
\[1\]
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