Properties of Exponents Warm Up Problem of the

Properties of Exponents Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Properties of Exponents Warm Up Evaluate. 1. 33 27 2. 4 • 4 • 4 256 3. b 2 for b = 4 16 4. n 2 r for n = 3 and r = 2 18

Properties of Exponents Problem of the Day Calculate 6 to the fourth power minus 56. 1240

Properties of Exponents Learn to apply the properties of exponents.

Properties of Exponents The factors of a power, such as 74, can be grouped in different ways. Notice the relationship of the exponents in each product. 7 • 7 • 7 = 74 (7 • 7) • 7 = 73 • 71 = 74 (7 • 7) • (7 • 7) = 72 • 72 = 74

Properties of Exponents

Properties of Exponents Additional Example 1: Multiplying Powers with the Same Base Multiply. Write the product as one power. A. 66 • 63 66 + 3 69 Add exponents. B. n 5 • n 7 n 5 + 7 n 12 Add exponents.

Properties of Exponents Additional Example 1: Multiplying Powers with the Same Base Continued Multiply. Write the product as one power. C. 25 • 2 25 + 1 26 Think: 2 = 2 1 Add exponents. D. 244 • 244 24 4 + 4 24 8 Add exponents.

Properties of Exponents Check It Out: Example 1 Multiply. Write the product as one power. A. 42 • 44 42 + 4 46 Add exponents. B. x 2 • x 3 x 2 + 3 x 5 Add exponents.

Properties of Exponents Check It Out: Example 1 Multiply. Write the product as one power. C. x 5 • y 2 Cannot combine; the bases are not the same. D. 412 • 417 41 2 + 7 41 9 Add exponents.

Properties of Exponents Notice what occurs when you divide powers with the same base. 5 5 55 2 = 5 5 = = = 5 5 5 53

Properties of Exponents Additional Example 2: Dividing Powers with the Same Base Divide. Write the quotient as one power. A. 5 7 3 7 75 – 3 7 Subtract exponents. 2 10 B. x 9 x x 10 – 9 x Subtract exponents. Think: x 1 = x

Properties of Exponents Check It Out: Example 2 Divide. Write the product as one power. A. 99 92 99 – 2 97 B. Subtract exponents. e 10 e 5 e 10 – 5 5 e Subtract exponents.

Properties of Exponents Reading Math 4 5 (9 ) is read as “nine to the fourth, to the fifth. ”

Properties of Exponents Additional Example 3: Raising a Power to a Power Simplify. A. (54)2 54 • 2 Multiply exponents. 58 B. (67)9 67 • 9 663 Multiply exponents.

Properties of Exponents Additional Example 3: Raising a Power to a Power Simplify. C. 2 3 12 – 3 Multiply exponents. 2 3 12 • – 3 D. (172)– 20 Multiply exponents. 172 • – 20 17– 40

Properties of Exponents Check It Out: Example 3 Simplify. A. (33)4 33 • 4 Multiply exponents. 312 B. (48)2 48 • 2 416 Multiply exponents.

Properties of Exponents Check It Out: Example 3 Simplify. C. 1 4 11 – 2 Multiply exponents. 1 4 11 • – 2 D. (134)– 10 Multiply exponents. 134 • – 10 13– 40

Properties of Exponents Lesson Quizzes Standard Lesson Quiz for Student Response Systems

Properties of Exponents Lesson Quiz Write the product or quotient as one power. 1. n 3 n 4 109 3. 105 n 7 104 2. 8 • 88 89 t 9 4. t 7 t 2 5. 32 • 33 • 35 310 6. (m 2)19 m 38 7. (9 -8)9 9– 72 8. (104)0 1