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Aman ϭ amϩn m 4. 1ab 2 n ϭ anbn a b n n a bn 2 To divide two powers of the same number, subtract the exponents. To raise a power to a new power, multiply the exponents. 2 ▼ P RO O F O F LAW 3 If m and n are positive integers, we have 1am 2 n ϭ 1a # a # p # a2 n 1442443 m factors ϭ 1a # a # p # a2 1a # a # p # a2 p 1a # a # p # a2 1442443 1442443 m factors 1442443 m factors m factors 144444444424444444443 n groups of factors ϭ a # a # p # a ϭ amn 1442443 mn factors The cases for which m Յ 0 or n Յ 0 can be proved by using the definition of negative exponents.

If x . 18 CHAPTER P | Prerequisites 6. The absolute value of the difference between a and b is (geometrically) the between them on the real number line. ▼ SKI LLS 7–8 Place the correct symbol 1Ͻ, Ͼ, or ϭ2 in the space. ■ 7. (a) 3 2 3 8. 67 0 33–38 ■ Express the interval in terms of inequalities, and then graph the interval. ✎ 33. 1Ϫ3, 02 34. 12, 84 35. 32, 82 36. ΄Ϫ6, Ϫ12΅ 37. 32, q 2 38. 1Ϫq, 1 2 39–44 ■ Express the inequality in interval notation, and then graph the corresponding interval. 39.

Since 1 itself is not in the interval, the interval has no largest number. 11, 32 പ 32, 74 ϭ 5x 0 1 Ͻ x Ͻ 3 and 2 Յ x Յ 76 ϭ 5x 0 2 Յ x Ͻ 36 ϭ 32, 32 This set is illustrated in Figure 7. (b) The union of two intervals consists of the numbers that are in either one interval or the other (or both). Therefore, 11, 32 ʜ 32, 74 ϭ 5x 0 1 Ͻ x Ͻ 3 or 2 Յ x Յ 76 ϭ 5x 0 1 Ͻ x Յ 76 ϭ 11, 7 4 This set is illustrated in Figure 8. 0001 _3 ✎ 7 FIGURE 8 11, 32 ʜ 32, 74 Practice what you’ve learned: Do Exercise 47.

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