1. Concept

2. Example 1 Quotient of Powers = xy 9 Simplify. Answer: = xy 9 Quotient of Powers Group powers that have the same base.

3. A.A B.B C.C D.D Example 1 A. B. C. D.

4. Concept

5. Example 2 Power of a Quotient Power of a Power Power of a Product Answer:

6. A.A B.B C.C D.D Example 2 A.AnsA B.AnsB C.AnsC D.AnsD Simplify

7. Concept (0 0 is undefined)

8. Example 3 Zero Exponent Answer: 1 A.

9. Example 3 Zero Exponent B. a 0 = 1 = nQuotient of Powers Simplify. Answer: n

10. A.A B.B C.C D.D Example 3 A. B.1 C.0 D.–1 A. Simplify. Assume that z is not equal to zero.

11. A.A B.B C.C D.D Example 3 A. B. C. D. B. Simplify. Assume that x and k are not equal to zero.

12. Concept

13. Example 4 Negative Exponents Negative Exponent Property A. Simplify. Assume that no denominator is equal to zero. Answer:

14. Example 4 Negative Exponents Group powers with the same base. B. Simplify. Assume that p, q and r are not equal to zero. Quotient of Powers and Negative Exponent Property

15. Example 4 Negative Exponents Negative Exponent Property Multiply. Simplify. Answer:

16. A.A B.B C.C D.D Example 4 A. Simplify. Assume that no denominator is equal to zero. A. B. C. D.

17. A.A B.B C.C D.D Example 4 A.AnsA B.AnsB C.AnsC D.AnsD B. Simplify. Assume that no denominator is equal to zero.

18. Vocabulary order of magnitude--An estimate of size or magnitude expressed as a power of ten: Earth's mass is of the order of magnitude of 10 22 tons; that of the sun is 10 27 tons.

19. Example 5 Apply Properties of Exponents SAVINGS Darin has $123,456 in his savings account. Tabo has $156 in his savings account. Determine the order of magnitude of Darin’s account and Tabo’s account. How many orders of magnitude as great is Darin’s account as Tabo’s account? UnderstandWe need to find the order of magnitude of the amounts of money in each account. Then find the ratio of Darin’s account to Tabo’s account. PlanRound each dollar amount to the nearest power of ten. Then find the ratio.

20. Example 5 Apply Properties of Exponents SolveThe amount in Darin’s account is close to $100,000. So, the order is 10 5. The amount in Tabo’s account is close to 100, so the order of magnitude is 10 2. The ratio of Darin’s account to Tabo’s account is or 10 3. Answer:So, Darin has 1000 times as much as Tabo, or Darin has 3 orders of magnitude as much in his account as Tabo.

21. Example 5 Apply Properties of Exponents CheckThe ratio of Darin’s account to Tabo’s account is ≈ 792. The power of ten closest to 792 is 1000 which has an order of magnitude of 10 3. 

22. A.A B.B C.C D.D Example 5 A circle has a radius of 210 centimeters. How many orders of magnitude as great is the area of the circle as the circumference of the circle? A.10 1 B.10 2 C.10 3 D.10 4