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

Check Skills/Warm Ups

Solutions = = = = = = = = = 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 m 6 m n 2 4 n 2 =

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Homework Solutions – , 80, , 96, , , –0.5, 0.25, – , 0.072, –48, 96, – geometric 14.arithmetic 15.geometric 16.arithmetic 17.arithmetic 18.geometric 19.5; 135; 10, –5; –135; –10, ; –135; –10, ; 13.5, –2; –250; –156,250

Homework (cont.) 24.–1.1; 70.4; 18, A(n) = n–1 ; A(n) = –6 2 n–1 ; – A(n) = 7 (1.1) n–1 ; x 10 z 20

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

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.

Key Concepts (cont.)

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:

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  10 7–5 = Subtract exponents when dividing powers with the same base  10 2 = Simplify the exponent  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!!

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

(a.) Simplify 2323 – = Raise the numerator and the denominator to the third power. Simplify or= Example 4: 2323 – = Rewrite using the reciprocal of 2323

(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

Simplify each expression a 8 a –2 w3w7w3w7 (3a) 4 (2a –2 ) 6a   10 – x 33x 24x 33x 2 a 10 1 w  or x 3 Try These: 2 –3

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