Chapter 7.5, Problem 12CB

To determine

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

Answer to Problem 12CB

  $a^y$ is greater than $a^x$ .

Explanation of Solution

Given information:

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

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 $a>1$ and $x<y$ , then $a^x<a^y$ because power $y$ of base $a$ is greater than power $x$ of same base $a$ .

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