8.1 Problem Solving Help
Help for Exercises 4651 on page 447
In Exercises 4651, you can use the Multiplication Properties of Exponents to simplify all expressions containing exponents. Refer to the summary box at the bottom of page 445 which lists these properties. Be sure to carefully apply the properties in the same way that they are shown. Each of the first three examples of Lesson 8.1 shows how to properly apply one of the properties to simplify an exponential expression. In some cases you will need to apply more than one property to simplify the expression, as shown in Example 4.
Once you have simplified each expression, you will need to decide which side is greater. Some of these are fairly straightforward. For example, the inequality 4^{5}7^{2} > 4^{3}7 is true because there are more factors of 4 and 7 on the lefthand side.
The inequality 4^{8 } 4^{2}3^{6}, however, may not be as easy. In this case, it is helpful to write the expression on the left side as 4^{2}4^{6}, giving the statement 4^{2}4^{6} 4^{2}3^{6}. Now you can see that both sides contain the expression 4^{2}. The remaining factor on the left side, 4^{6}, is clearly larger than 3^{6}. Therefore, the inequality statement should be written as 4^{8 } > 4^{2}3^{6}. You may wish to evaluate each expression of an inequality to be sure your answer is correct.
