Assume the result of (a) and prove (b)
(a) Prove that if 0 <= a < b, then a^n < b^n.
(b) Prove that every nonnegative real number x has a unique nonnegative nth root x^1/n.
HINT: The existence of x^1/n can be seen by applying the intermediate-value theorem to the function f (t) = t^n for t >= 0. The uniqueness follows from (a).
Does anyone have idea how to do this?