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x = y^a, y = z^b, z = x^c: find abc

The same question, asked 2 times: CDS 1 2018, CDS 2 2018. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 1 2018

    3
    If x=y1/ax = y^{1/a}, y=z1/by = z^{1/b} and z=x1/cz = x^{1/c} where x≠1x \ne 1, y≠1y \ne 1, z≠1z \ne 1, then what is the value of abcabc?

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  2. Question 2

    CDS 2 2018

    2
    If x=yax = y^a, y=zby = z^b and z=xcz = x^c, then the value of abc is

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