If `xy+z=y`, what is x in terms of y and z?

If (z^(x ^(2 ) +y ^(2)))/(z ^(-2xy ))= (z ^(3)), x and y are positive integers, and x gt y, what is the value of x -y ?

If (xy)^a=z,(yz)^a=x, and (xz)^a=y , then what is the value of a? (None of x,y and z is either 0 or 1.)

If x,y and z are positive integers such that x < y < z and x + y + z = 6 , then what is the value of z?

If (x^y)^z = x^y ^ ^z where each of x, y and z is greater than 1, then find y in terms of z.