Question

why is (xyz)^4 = x^4 y^4 z^4

Answer 1

They are treated as one thing and when you do the expanded version it is becomes (xyz)*(xyz)*(xyz)*(xyz) which is just x*x*x*x*y*y*y*y*z*z*z*z. Which x^(4)*y^(4)*z^(4) is just x*x*x*x*y*y*y*y*z*z*z*z.