Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{{x}^{2(a+b)}{({x}^{2})}^{b+c}{({x}^{2})}^{c+a}}{{({x}^{a}{x}^{b}{x}^{c})}^{4}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{{x}^{2(a+b)}{x}^{2(b+c)}{({x}^{2})}^{c+a}}{{({x}^{a}{x}^{b}{x}^{c})}^{4}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{{x}^{2(a+b)}{x}^{2(b+c)}{x}^{2(c+a)}}{{({x}^{a}{x}^{b}{x}^{c})}^{4}}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{{x}^{2(a+b)+2(b+c)+2(c+a)}}{{({x}^{a}{x}^{b}{x}^{c})}^{4}}\]
Expand.
\[\frac{{x}^{2a+2b+2b+2c+2c+2a}}{{({x}^{a}{x}^{b}{x}^{c})}^{4}}\]
Collect like terms.
\[\frac{{x}^{(2a+2a)+(2b+2b)+(2c+2c)}}{{({x}^{a}{x}^{b}{x}^{c})}^{4}}\]
Simplify \((2a+2a)+(2b+2b)+(2c+2c)\) to \(4a+4b+4c\).
\[\frac{{x}^{4a+4b+4c}}{{({x}^{a}{x}^{b}{x}^{c})}^{4}}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{{x}^{4a+4b+4c}}{{({x}^{a+b+c})}^{4}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{{x}^{4a+4b+4c}}{{x}^{(a+b+c)\times 4}}\]
Regroup terms.
\[\frac{{x}^{4a+4b+4c}}{{x}^{4(a+b+c)}}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[{x}^{4a+4b+4c-4(a+b+c)}\]
Expand.
\[{x}^{4a+4b+4c-4a-4b-4c}\]
Collect like terms.
\[{x}^{(4a-4a)+(4b-4b)+(4c-4c)}\]
Simplify \((4a-4a)+(4b-4b)+(4c-4c)\) to \(0\).
\[{x}^{0}\]
Use Rule of Zero: \({x}^{0}=1\).
\[1\]
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