Chapter 4.5, Problem 64E

To determine

To simplify $\frac{a^{m+n}}{a^n}$

Answer to Problem 64E

  $a^m$

Explanation of Solution

Given information: Simplify $\frac{a^{m+n}}{a^n}$

This answer shall be derived using the product of powers rule, wherein the exponents of a common base can be added during multiplication and subtracted during division.

Calculation:

Given, $\frac{a^{m+n}}{a^n}$

  $=a^{m+n-n}$ Here, the Rule of exponents is used wherein the exponents are added if there is multiplication of a common base, and/or subtracting the exponents if there divisions of two common bases.

  $=a^m$ This is the simplified expression