Chapter 4.3, Problem 47WE

To determine

To simplify the expression

  $a^x\cdot a^3$

Answer to Problem 47WE

  $a^{x+3}$

Explanation of Solution

Given:

  $a^x\cdot a^3$

Concept Used:

• For all positive integers m and n: ${\left(a^m\right)}^n=a^{mn}$
• For all integers m and n : $a^m{a}^n=a^{m+n}$
• For all integers m and n : ${\left(ab\right)}^n=a^n{b}^n$

Calculation:

To simplify the expression

  $a^x\cdot a^3$

Use the basic properties of power.

First simplify this using the property $a^m{a}^n=a^{m+n}$ and then proceed further to simplify, as

  $a^x\cdot a^3=a^{x+3}$

Now the above expression can’t be simplified further.

Thus, simplified form of given expression is

  $a^x\cdot a^3=a^{x+3}$