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Question
Prove that:
`(x^a/x^b)^cxx(x^b/x^c)^axx(x^c/x^a)^b=1`
Solution
Consider the left hand side:
`(x^a/x^b)^cxx(x^b/x^c)^axx(x^c/x^a)^b=1`
`=x^(ac)/x^(bc)xxx^(ba)/x^(ca)xxx^(cb)/x^(ab)`
`=(x^(ac)xxx^(ba)xxx^(cb))/(x^(bc)xxx^(ca)xxx^(ab))`
`=x^(ac+ba+cb)/x^(bc+ca+ab)`
= 1
Left hand side is equal to right hand side.
Hence proved.
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