Textbook Problem

a. Let m be any positive integer, and define $f\left(x\right)=x^m$

for each nonnegative real number x. Use the binomial theorem to show that f is an increasing function.
b. Let in and ii be any positive integers, and let $g\left(x\right)=x^{m/n}$for each nonnegative real number x. Prove that g is an increasing function.
Note: The results of exercise 21 are used in the exercises for Sections 11.2 and 11.4.