Chapter 1 - Section 1.8 - Inequalities - 1.8 Exercises - Page 91: 126

For any $a^n$ and $b^n$, when $a0$ and $b>0$ $a^n>b^n$ when $n$ is even; $a<0$ and $b<0$

Let's consider several cases. At first "critical" points like $-1; 0; 1$, then number between $0$ and $1$ and some random numbers. $a=-1$ ; $b=1$ || $a0$ and $b>0$ $a^n>b^n$ when $n$ is even; $a<0$ and $b<0$