Chapter 2.2, Problem 19E

Let $x\text{and}y$ be integers, and let $m\text{and}n$ be positive integers. Use induction to prove the statements in Exercises $18-23$. ( The definitions of $x^n$ and $nx$ are given before Theorem $2.5$ in Section $2.1$.)

$x^m\cdot x^n=x^{m+n}$