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Question
Show that:
`(x^(1/(a-b)))^(1/(a-c))(x^(1/(b-c)))^(1/(b-a))(x^(1/(c-a)))^(1/(c-b))=1`
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Solution
`(x^(1/(a-b)))^(1/(a-c))(x^(1/(b-c)))^(1/(b-a))(x^(1/(c-a)))^(1/(c-b))=1`
LHS = `(x^(1/(a-b)))^(1/(a-c))(x^(1/(b-c)))^(1/(b-a))(x^(1/(c-a)))^(1/(c-b))`
`=(x)^(1/(a-b)xx1/(a-c))(x)^(1/(b-c)xx1/(b-a))(x)^(1/(c-a)xx1/(c-b))`
`=(x)^(1/(a-b)xx1/(a-c)+1/(b-c)xx1/(b-a)+1/(c-a)xx1/(c-b))`
`=(x)^(((b-c)-(a-c)+(a-b))/((a-b)(a-c)(b-c)))`
`=x^0`
= 1
= RHS
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