The following is the problem on 63rd page of Zakon's "Basic Mathematics"
(iii) If x > y ≥ 0, then
x2 > y2 and x3 > y3 ≥ 0 (where x3 = x2x);
x4 > y4 ≥ 0 (where x4 = x3x).
Which (if any) of these propositions remain valid also if x or y is negative? Give proof.
I am able to solve the first part of the problem. Got stuck in the second. If somebody can give me a hint of how to determine whether the proposition is valid if x or y is negative.