Chapter 7.5, Problem 13CB

To determine

To find: the greater, $x^a$ or $y^a$ .

Answer to Problem 13CB

  $y^a$ is greater than $x^a$ .

Explanation of Solution

Given information:

If $1<x<y$ and $a>1$ .

Calculation:

The pattern for increasing positive power of same base keeps increasing to the right side of the number line and for negative powers $a^{-n}$ is closest to 0 where $n$ is the highest number of all.

Consider the following conditions provided in the textbook.

If $1<x<y$ and $a>1$ , then

  $x^a<y^a$ because power base $y$ is greater than base $x$ .

Hence, $y^a$ is greater than $x^a$ .