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4-3

4-3. Properties of Exponents. Course 3. Warm Up. Problem of the Day. Lesson Presentation. Warm Up Evaluate. 27. 1. 3 3. 2. 4 • 4 • 4 • 4. 256. 3. b 2 for b = 4 . 16. 4. n 2 r for n = 3 and r = 2. 18. Problem of the Day Calculate 6 to the fourth power minus 56.

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4-3

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  1. 4-3 Properties of Exponents Course 3 Warm Up Problem of the Day Lesson Presentation

  2. Warm Up Evaluate. 27 1. 33 2. 4 • 4 • 4 • 4 256 3.b2 for b = 4 16 4. n2r for n = 3 and r = 2 18

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

  4. Learn to apply the properties of exponents.

  5. 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 • 7 = 74 (7 • 7 • 7) • 7 = 73 • 71 = 74 (7 • 7) • (7 • 7) = 72 • 72 = 74

  6. A. 66 •63 6 6+ 3 6 9 n 5 + 7 n 12 Additional Example 1: Multiplying Powers with the Same Base Multiply. Write the product as one power. Add exponents. B. n5 •n7 Add exponents.

  7. 1 Think: 2 = 2 2 5 + 1 2 6 24 4 + 4 24 8 Additional Example 1: Multiplying Powers with the Same Base Continued Multiply. Write the product as one power. C. 25 • 2 Add exponents. D.244• 244 Add exponents.

  8. A. 42 •44 4 2 + 4 4 6 x 2 + 3 x 5 Check It Out: Example 1 Multiply. Write the product as one power. Add exponents. B. x2 •x3 Add exponents.

  9. 41 2 + 7 41 9 Check It Out: Example 1 Multiply. Write the product as one power. C. x5 • y2 Cannot combine; the bases are not the same. x5 • y2 D.412• 417 Add exponents.

  10. 5555 5 5555 5 5 5 = = = 5 •5 = 52 555 555 53 Notice what occurs when you divide powers with the same base.

  11. 5 – 3 10 – 9 x 7 9 10 3 2 5 7 x x 7 7 Think: x = x 1 Additional Example 2: Dividing Powers with the Same Base Divide. Write the quotient as one power. A. Subtract exponents. B. Subtract exponents. x

  12. 9 – 2 9 10 – 5 e 5 e Check It Out: Example 2 Divide. Write the product as one power. 9 9 A. 9 2 Subtract exponents. 97 e 10 B. e 5 Subtract exponents.

  13. Reading Math 5 4 (9 ) is read as “nine to the fourth, to the fifth.” RAISING A POWER TO A POWER

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

  15. 2 3 2 3 12 –3 12 • –3 = –36 2 3 = Additional Example 3: Raising a Power to a Power Simplify. D. (172) –20 C. (172) –20 Multiply exponents. Multiply exponents. = 172 • –20 = 17–40

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

  17. 1 4 1 4 11 –2 11• –2 = –22 1 4 = Check It Out: Example 3 Simplify. D. (134) –10 C. (134) –10 Multiply exponents. Multiply exponents. = 134 • –10 = 13–40

  18. n 7 8 9 109 4 10 105 t 2 t9 t7 3 10 Lesson Quiz Write the product or quotient as one power. 1. n3n4 2. 8 • 88 4. 3. 6. (m2)19 m38 5. 32 • 33 • 35 8. (104)0 1 7. (9-8)9 9–72

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