if ax = b, by= c and xyz = 1, then what is the value of cz?

Given, xyz = 1, a^x = b, b^y = c
Now, b = a^x
Apply the law of algebra .
Take the power y of both side equation.
⇒ b^y= a^xy
Take the power z of both side equation.
⇒ b^yz = a^xyz
⇒ ( b^y )^z = a^xyz
Replace the b^y with c and xyz with 1 as per given equation,
⇒ c^z = a