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Question
Show that:
`(x^(a-b))^(a+b)(x^(b-c))^(b+c)(x^(c-a))^(c+a)=1`
Solution
`(x^(a-b))^(a+b)(x^(b-c))^(b+c)(x^(c-a))^(c+a)=1`
LHS = `(x^(a-b))^(a+b)(x^(b-c))^(b+c)(x^(c-a))^(c+a)`
`=[x^((a-b)(a+b))][x^((b-c)(b+c))][x^((c-a)(c+a))]`
`=x^((a^2-b^2))x^((b^2-c^2))x^((c^2-a^2))`
`=x^(a^2-b^2+b^2-c^2+c^2-a^2)`
`=x^0`
= 1
= RHS
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