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Question
Simplify:
`(x^(a+b)/x^c)^(a-b)(x^(b+c)/x^a)^(b-c)(x^(c+a)/x^b)^(c-a)`
Solution
`(x^(a+b)/x^c)^(a-b)(x^(b+c)/x^a)^(b-c)(x^(c+a)/x^b)^(c-a)`
`=(x^((a+b)(a-b))/x^(c(a-b)))(x^((b+c)(b-c))/x^(a(b-c)))(x^((c+a)(c-a))/x^(b(c-a)))`
`=(x^(a^2-b^2)/x^(ca-bc))(x^(b^2-c^2)/x^(ab-ac))(x^(c^2-a^2)/x^(bc-ab))`
`=x^(a^2-b^2+b^2-c^2+c^2-a^2)/x^(ca-bc+ab-ac+bc-ab)`
`=x^0/x^0`
= 1
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