Question 190125
Let 
{{{ x^(1/p)=y^(1/q)=z^(1/r)=t }}}
Then
from {{{ x^(1/p)=t }}}, we obtain {{{x=t^p}}}
For the same reason, we have
{{{y=t^q}}}
and
{{{z=t^r}}}
Substituting them into {{{xyz=1}}}, we have
{{{(t^p)(t^q)(t^r)=1}}}, or written as:
{{{t^(p+q+r)=1}}}
The equation implies that:
{{{p+q+r=0}}}