Simplify: ${(x^{a})}^{b - c} {(x^{b})}^{c - a} {(x^{c})}^{a - b}$

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Solution

${(x^{a})}^{b - c} {(x^{b})}^{c - a} {(x^{c})}^{a - b}$

$= (x^{a b - a c}) (x^{b c - b a}) (x^{c a - c b})$

$= x^{a b - a c + b c - b a + c a - c b}$

$= x^{0} = 1$

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