Problem Solving with Subgoals in Expressions and Rational Exponents

1. Chapter 5 Section 5.7

2. Objectives • To solve problems by identifying and achieving subgoals. • To write expressions with rational exponents in simplest radical form and vice versa. • To evaluate expressions in either exponential or radical form.

3. Subgoals Like a good mystery that enfolds little by little, page by page, a good problem solver approaches a problem using a series of small steps or subgoals. By doing so, you make problem solving a simpler process.

4. Example Economists refer to inflation as increases in the average cost of consumer items at some projected time. In this formula, C represents the projected cost of the item at a given annual inflation rate, cthe present cost of the item, r the rate of inflation (in decimal form), and n the number of years for the projection. Suppose a gallon of milk costs $2.69 now. How much would the price increase in 6 months with an inflation rate of 5.3%? Subgoal 1: Identify the known values. Subgoal 2: Find the value of C. Subgoal 3: Find the increase in cost.

5. Definition of For any real number b and for any integer n > 1, = Except when b < 0 and n is even.

6. Definitions of Rational Exponents For any nonzero real number b, and any integers m and n, with n > 1, = = ()m Except when b < 0 and n is even.

7. Examples

8. Practice Pg 300 numbers 14-23