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If a^(x)=b, b^(y)=c,c^(z)=a, prove that ...

If `a^(x)=b, b^(y)=c,c^(z)=a,` prove that `xyz = 1` where `a,b,c` are distinct numbers

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We have, `a^(xyz)=(a^(x))^(yz)`
`rArr a^(xyz)=(b)^(yz)[ :' a^(x)=b]`
`rArr a^(xyz)=(b^(y))^(z)`
`rArr a^(xyz)=c^(z) [ :'b^(y)=c]`
`rArr a^(xyz)=a[ :' c^(z)=a]`
`:. A^(xyz)=a^(1)`
`rArr xyz=1`
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