1. 8-5: Division Properties of Exponents Objectives: 1.To divide powers with the same base. 2.To raise a quotient to a power.

2. Check Skills/Warm Ups

3. Solutions 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. = 5 20 5 1 5 4 1414 125 25 25 5 25 1 = = 5 60 100 20 3 20 5 3535 = 124 4 = = 31 4 31 4 1 6 15 2525 3 2 3 5 = 8 30 2 4 2 15 4 15 10 35 2727 5 2 5 7 = 18 63 2727 9 2 9 7 = 5xy 15x y3y3 5 x y 5 3 x = 6y23x6y23x 2y2x2y2x 3 2 y 2 3 x = 3ac 12a 3 a c 3 4 a c4c4 = 24m 6mn 2 6 4 m 6 m n 2 4 n 2 =

4. Questions??

5. Homework Solutions 1.4 2.4 3.0.1 4.2.50 5.–0.25 6.2 7.40, 80, 160 8.48, 96, 192 9.20.25, 30.375, 45.5625 10.–0.5, 0.25, –0.125 11.0.36, 0.072, 0.0144 12.–48, 96, –192 13.geometric 14.arithmetic 15.geometric 16.arithmetic 17.arithmetic 18.geometric 19.5; 135; 10,935 20.–5; –135; –10,935 21.5; –135; –10,935 22.0.5; 13.5, 1093.5 23.–2; –250; –156,250

6. Homework (cont.) 24.–1.1; 70.4; 18,022.4 25.A(n) = 6 0.5 n–1 ; 0.37 26.A(n) = –6 2 n–1 ; –3072 27.A(n) = 7 (1.1) n–1 ; 9.317 1 x 10 z 20

7. Questions??

8. 8-5: Division Properties of Exponents Objectives: 1.To divide powers with the same base. 2.To raise a quotient to a power.

9. Key Concepts *You can use repeated multiplication to simplify fractions. Expand the numerator and the denominator using repeated multiplication. Then cancel like terms. Like this: *Since division by zero is undefined, assume that no variable is equal to zero.

10. Key Concepts (cont.)

11. Simplify each expression. x4x9x4x9 a. Simplify the exponents.= x –5 Rewrite using positive exponents. 1 x 5 = p 3 j –4 p –3 j 6 = p 6 j –10 Simplify. Rewrite using positive exponents. p 6 j 10 = b. = Subtract exponents when dividing powers with the same base. x 4 – 9 = Subtract exponents when dividing powers with the same base. p 3 – (–3) j –4 – 6 Example 1:

12. A small dog’s heart beats about 64 million beats in a year. If there are about 530 thousand minutes in a year, what is its average heart rate in beats per minute? 64 million beats 530 thousand min 6.4  10 7 beats 5.3  10 5 min =Write in scientific notation. 6.4 5.3  10 7–5 = Subtract exponents when dividing powers with the same base. 6.4 5.3  10 2 = Simplify the exponent. 1.21  10 2 Divide. Round to the nearest hundredth. = 121 Write in standard notation. The dog’s average heart rate is about 121 beats per minute. Example 2: Oh No, A Word Problem!!

13. Simplify 3 y 3 4 3 4 y 12 =Multiply the exponent in the denominator. 81 y 12 = Simplify. Example 3: 3 y 3 4 3434 (y 3)4(y 3)4 = Raise the numerator and the denominator to the fourth power.

14. (a.) Simplify 2323 –3 3 33233323 = Raise the numerator and the denominator to the third power. Simplify. 27 8 3 3838 or= Example 4: 2323 –3 3232 3 = Rewrite using the reciprocal of 2323

15. (b.) Simplify Raise the numerator and denominator to the second power. (–c) 2 (4b) 2 = Simplify. c 2 16b 2 = Example 4: (continued) 4bc4bc – 4bc4bc – –2 c4b c4b – 2 = Rewrite using the reciprocal of. 4bc4bc – Write the fraction with a negative numerator. c 4b – 2 = –2

16. Simplify each expression. 1.2.3. 4.5.6. a 8 a –2 w3w7w3w7 (3a) 4 (2a –2 ) 6a 2 1.6  10 3 4  10 –2 245245 4x 33x 24x 33x 2 a 10 1 w 4 27 4  10 4 256 25 or 10 6 25 27 64x 3 Try These: 2 –3

17. Questions?

18. HW #41: p. 420 #2-36even, 43-46, 52, 53, 56, 59