[warut]

$$ \frac{(b^y)^z}{(c^z)^y} a^{x+y+z} = \Big( \frac{c}{a} \Big)^z \Big( \frac{b}{a} \Big)^y a^{x+y+z} = c^zb^ya^x = \frac{a}{b} \cdot \frac{c}{a} \cdot \frac{b}{c} =1$$