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Warm Up

Apply Exponent Properties Involving Quotients. Warm Up. Lesson Presentation. Lesson Quiz. 1. 1. q 3 when q =. 4. 3. 1. 9. ANSWER. 5. 64. 25. 2. c 2 when c =. ANSWER. Warm-Up. Evaluate the expression. about 10 6 or 1,000,000. ANSWER. Warm-Up.

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Warm Up

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  1. Apply Exponent Properties Involving Quotients Warm Up Lesson Presentation Lesson Quiz

  2. 1 1.q3whenq = 4 3 1 9 ANSWER 5 64 25 2.c2whenc = ANSWER Warm-Up Evaluate the expression.

  3. about 106or 1,000,000 ANSWER Warm-Up 3.A magazine had a circulation of 9364 in 2001. The circulation was about 125 times greater in 2006.Use order of magnitude to estimate the circulation in 2006.

  4. x6 a. d. x6 = x4 (– 3)9 b. (– 3)3 512 1 810 57 x4 84 54 58 = c. 57 Example 1 Simplify the expression. = 810– 4 = (– 3)9 – 3 = 86 = (– 3)6 = 512 – 7 = x6 – 4 = 55 = x2

  5. 1. 4. y8 (– 4)9 2. (– 4)2 1 611 y5 65 94 93 92 3. Guided Practice Simplify the expression. = 66 = (– 4)7 = 95 = y3

  6. 3 a. = – 7 (– 7)2 49 x x2 x2 7 x3 x 2 2 y3 x y – = = = b. Example 2 Simplify the expression.

  7. 3 4x2 (4x2)3 64x6 a. = a8 5y 125y3 (5y)3 = 2b5 43 (x2)3 = 53y3 = 1 1 a10 a2 (a2)5 2a2 b5 2a2 1 b 5 b. = 2a2 b5 = a10 2a2b5 = Example 3 Simplify the expression. Power of a quotient property Power of a product property Power of a power property Power of a quotient property Power of a power property Multiply fractions. Quotient of powers property

  8. x2 4y 8. 3t 16 2 5. = 125 y3 3 – – = 6. a2 a 5 3 2s t5 y b b2 2 7. x4 = s3 t2 16y2 54 = Guided Practice Simplify the expression.

  9. To construct what is known as a fractal tree, begin with a single segment (the trunk) that is 1 unit long, as in Step 0. Add three shorter segments that are unit long to form the first set of branches, as in Step 1. Then continue adding sets of successively shorter branches so that each new set of branches is half the length of the previous set, as in Steps 2 and 3. 1 2 Example 4 FRACTAL TREE

  10. a. Make a table showing the number of new branches at each step for Steps 1  4. Write the number of new branches as a power of 3. How many times greater is the number of new branches added at Step 5 than the number of new branches added at Step 2? b. Example 4

  11. b. The number of new branches added at Step 5 is 35. The number of new branches added at Step 2 is 32. So, the number of new branches added at Step 5 is = 33 = 27 times the number of new branches added at Step 2. 35 32 Example 4 SOLUTION a.

  12. 9. FRACTAL TREE In Example 4, add a column to the table for the length of the new branches at each step. Write the length of the new branches as power of . What is the length of a new branch added at Step 9? 1 1 ( ) 2 9 = 2 1 units 512 Guided Practice SOLUTION

  13. Example 5 ASTRONOMY The luminosity (in watts) of a star is the total amount of energy emitted from the star per unit of time. The order of magnitude of the luminosity of the sun is 1026 watts. The star Canopus is one of the brightest stars in the sky. The order of magnitude of the luminosity of Canopus is 1030 watts. How many times more luminous is Canopus than the sun?

  14. Luminosity of Canopus (watts) 1030 1030 - 26 104 = = = Luminosity of the sun (watts) 1026 ANSWER Canopus is about 104 times as luminous as the sun. Example 5 SOLUTION

  15. ANSWER Canopus is about 102 times as luminous as Sirius. Guided Practice 9. WHAT IF? Sirius is considered the brightest star in the sky. Sirius is less luminous than Canopus, but Sirius appears to be brighter because it is much closer to the Earth. The order of magnitude of the luminosity of Sirius is 1028 watts. How many times more luminous is Canopus than Sirius?

  16. 63 65 –1 1.Simplify . 64 10 ANSWER ANSWER 64 103 4. 2.Simplify 107 3. s8 3.Simplify 3r s24 ANSWER 27r3 Lesson Quiz

  17. The order of magnitude of the power output of a nuclear-powered aircraft carrier is about 106watts. The order of magnitude of peak power at Hoover Dam is about 109 watts. How many times as great is the power output of Hoover Dam as the power output of a nuclear-powered aircraft carrier? 4. 103 ANSWER Lesson Quiz

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