7 4 Division Propertiesofof Exponents Warm Up Lesson

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7 -4 Division. Propertiesofof. Exponents Warm Up Lesson Presentation Lesson Quiz Holt Algebra 11

7 -4 Division. Propertiesofof. Exponents Warm Up Lesson Presentation Lesson Quiz Holt Algebra 11

7 -4 Division Properties of Exponents Warm Up Simplify. 1. (x 2)3 x 6

7 -4 Division Properties of Exponents Warm Up Simplify. 1. (x 2)3 x 6 2. 3. 4. 5. 6. Write in Scientific Notation. 7. 8. Holt Algebra 1

7 -4 Division Properties of Exponents Objective Use division properties of exponents to evaluate

7 -4 Division Properties of Exponents Objective Use division properties of exponents to evaluate and simplify expressions. Holt Algebra 1

7 -4 Division Properties of Exponents A quotient of powers with the same base

7 -4 Division Properties of Exponents A quotient of powers with the same base can be found by writing the powers in a factored form and dividing out common factors. Notice the relationship between the exponents in the original quotient and the exponent in the final answer: 5 – 3 = 2. Holt Algebra 1

7 -4 Division Properties of Exponents Holt Algebra 1

7 -4 Division Properties of Exponents Holt Algebra 1

7 -4 Division Properties of Exponents Example 1: Finding Quotients of Powers Simplify. A.

7 -4 Division Properties of Exponents Example 1: Finding Quotients of Powers Simplify. A. Holt Algebra 1 B.

7 -4 Division Properties of Exponents Example 1: Finding Quotients of Powers Simplify. C.

7 -4 Division Properties of Exponents Example 1: Finding Quotients of Powers Simplify. C. Holt Algebra 1 D.

7 -4 Division Properties of Exponents Helpful Hint Both Holt Algebra 1 and 729

7 -4 Division Properties of Exponents Helpful Hint Both Holt Algebra 1 and 729 are considered to be simplified.

7 -4 Division Properties of Exponents Check It Out! Example 1 Simplify. a. Holt

7 -4 Division Properties of Exponents Check It Out! Example 1 Simplify. a. Holt Algebra 1 b.

7 -4 Division Properties of Exponents Check It Out! Example 1 Simplify. c. Holt

7 -4 Division Properties of Exponents Check It Out! Example 1 Simplify. c. Holt Algebra 1 d.

7 -4 Division Properties of Exponents Example 2: Dividing Numbers in Scientific Notation Simplify

7 -4 Division Properties of Exponents Example 2: Dividing Numbers in Scientific Notation Simplify and write the answer in scientific notation Write as a product of quotients. Simplify each quotient. Simplify the exponent. Write 0. 5 in scientific notation as 5 x 10. The second two terms have the same base, so add the exponents. Simplify the exponent. Holt Algebra 1

7 -4 Division Properties of Exponents Writing Math You can “split up” a quotient

7 -4 Division Properties of Exponents Writing Math You can “split up” a quotient of products into a product of quotients: Example: Holt Algebra 1

7 -4 Division Properties of Exponents Check It Out! Example 2 Simplify and write

7 -4 Division Properties of Exponents Check It Out! Example 2 Simplify and write the answer in scientific notation. Write as a product of quotients. Simplify each quotient. Simplify the exponent. Write 1. 1 in scientific notation as 11 x 10. The second two terms have the same base, so add the exponents. Simplify the exponent. Holt Algebra 1

7 -4 Division Properties of Exponents Example 3: Application The Colorado Department of Education

7 -4 Division Properties of Exponents Example 3: Application The Colorado Department of Education spent about dollars in fiscal year 2004 -05 on public schools. There were about students enrolled in public school. What was the average spending per student? Write your answer in standard form. To find the average spending per student, divide the total debt by the number of students. Write as a product of quotients. Holt Algebra 1

7 -4 Division Properties of Exponents Example 3 Continued The Colorado Department of Education

7 -4 Division Properties of Exponents Example 3 Continued The Colorado Department of Education spent about dollars in fiscal year 2004 -05 on public schools. There were about students enrolled in public school. What was the average spending per student? Write your answer in standard form. To find the average spending per student, divide the total debt by the number of students. = 0. 58 × 109– 5 Simplify each quotient. = 0. 58 × 104 Simplify the exponent. Write in standard form. = 5800 The average spending per student is $5800. Holt Algebra 1

7 -4 Division Properties of Exponents Check It Out! Example 3 In 1990, the

7 -4 Division Properties of Exponents Check It Out! Example 3 In 1990, the United States public debt was about dollars. The population of the United States was about people. What was the average debt person? Write your answer in standard form. To find the average debt person, divide the total debt by the number of people. Write as a product of quotients. Holt Algebra 1

7 -4 Division Properties of Exponents Check It Out! Example 3 Continued In 1990,

7 -4 Division Properties of Exponents Check It Out! Example 3 Continued In 1990, the United States public debt was about dollars. The population of the United States was about people. What was the average debt person? Write your answer in standard form. To find the average debt person, divide the total debt by the number of people. Simplify each quotient. Simplify the exponent. Write in standard form. The average debt person was $12, 800. Holt Algebra 1

7 -4 Division Properties of Exponents A power of a quotient can be found

7 -4 Division Properties of Exponents A power of a quotient can be found by first writing the numerator and denominator as powers. Notice that the exponents in the final answer are the same as the exponent in the original expression. Holt Algebra 1

7 -4 Division Properties of Exponents Holt Algebra 1

7 -4 Division Properties of Exponents Holt Algebra 1

7 -4 Division Properties of Exponents Example 4 A: Finding Positive Powers of Quotient

7 -4 Division Properties of Exponents Example 4 A: Finding Positive Powers of Quotient Simplify. Use the Power of a Quotient Property. Simplify. Holt Algebra 1

7 -4 Division Properties of Exponents Example 4 B: Finding Positive Powers of Quotient

7 -4 Division Properties of Exponents Example 4 B: Finding Positive Powers of Quotient Simplify. Use the Power of a Quotient Property. Use the Power of a Product Property: Simplify and use the Power of a Power Property: Holt Algebra 1

7 -4 Division Properties of Exponents Example 4 C: Finding Positive Powers of Quotient

7 -4 Division Properties of Exponents Example 4 C: Finding Positive Powers of Quotient Simplify. Use the Power of a Quotient Property. Use the Power of a Product Property: Holt Algebra 1

7 -4 Division Properties of Exponents Example 4 C Continued Simplify and use the

7 -4 Division Properties of Exponents Example 4 C Continued Simplify and use the Power of a Power Property: . Use the Power of a Product Property: (x 3 y 3)2 = x 3 2 y 3 2. Simplify. Holt Algebra 1

7 -4 Division Properties of Exponents Check It Out! Example 4 a Simplify. Use

7 -4 Division Properties of Exponents Check It Out! Example 4 a Simplify. Use the Power of a Quotient Property. Simplify. Holt Algebra 1

7 -4 Division Properties of Exponents Simplify. Holt Algebra 1 Check It Out! Example

7 -4 Division Properties of Exponents Simplify. Holt Algebra 1 Check It Out! Example 4 b

7 -4 Division Properties of Exponents Simplify. Holt Algebra 1 Check It Out! Example

7 -4 Division Properties of Exponents Simplify. Holt Algebra 1 Check It Out! Example 4 c

7 -4 Division Properties of Exponents Remember that . What if x is a

7 -4 Division Properties of Exponents Remember that . What if x is a fraction? Write the fraction as division. Use the Power of a Quotient Property. Multiply by the reciprocal. Simplify. Use the Power of a Quotient Property. Therefore, Holt Algebra 1 .

7 -4 Division Properties of Exponents Holt Algebra 1

7 -4 Division Properties of Exponents Holt Algebra 1

7 -4 Division Properties of Exponents Example 5 A: Finding Negative Powers of Quotients

7 -4 Division Properties of Exponents Example 5 A: Finding Negative Powers of Quotients Simplify. Rewrite with a positive exponent. Use the Power of a Quotient Property. and Holt Algebra 1

7 -4 Division Properties of Exponents Example 5 B: Finding Negative Powers of Quotients

7 -4 Division Properties of Exponents Example 5 B: Finding Negative Powers of Quotients Simplify. Use the Power of a Quotient Property. Use the Power of a Power Property (y 3)2 = y 3 2 = y 6. Use the Power of a Product Property (2 x 2)2 = 22 x 2 2 Simplify. Holt Algebra 1

7 -4 Division Properties of Exponents Example 5 C: Finding Negative Powers of Quotients

7 -4 Division Properties of Exponents Example 5 C: Finding Negative Powers of Quotients Simplify. Rewrite each fraction with a positive exponent. Use the Power of a Quotient Property. Use the Power of a Product Property: (2 n)3 = 23 n 3 and (6 m)3 = 63 m 3. Holt Algebra 1

7 -4 Division Properties of Exponents Example 5 C: Finding Negative Powers of Quotients

7 -4 Division Properties of Exponents Example 5 C: Finding Negative Powers of Quotients Simplify. 1 1 1 2 24 Divide out common factors. 12 Simplify. Holt Algebra 1

7 -4 Division Properties of Exponents Helpful Hint Whenever all of the factors in

7 -4 Division Properties of Exponents Helpful Hint Whenever all of the factors in the numerator or the denominator divide out, replace them with 1. Holt Algebra 1

7 -4 Division Properties of Exponents Check It Out! Example 5 a Simplify. Rewrite

7 -4 Division Properties of Exponents Check It Out! Example 5 a Simplify. Rewrite with a positive exponent. Use the Power of a Quotient Property. 93 = 729 and 43 = 64. Holt Algebra 1

7 -4 Division Properties of Exponents Check It Out! Example 5 b Simplify. Rewrite

7 -4 Division Properties of Exponents Check It Out! Example 5 b Simplify. Rewrite with a positive exponent. Use the Power of a Quotient Property. Use the Power of a Product Property: (b 2 c 3)4= b 2 • 4 c 3 • 4 = b 8 c 12 and (2 a)4= 24 a 4 = 16 a 4. Holt Algebra 1

7 -4 Division Properties of Exponents Simplify. Check It Out! Example 5 c Rewrite

7 -4 Division Properties of Exponents Simplify. Check It Out! Example 5 c Rewrite each fraction with a positive exponent. Use the Power of a Quotient Property. Simplify. Add exponents and divide out common terms. Holt Algebra 1

7 -4 Division Properties of Exponents Lesson Quiz: Part I Simplify. 1. 2. 3.

7 -4 Division Properties of Exponents Lesson Quiz: Part I Simplify. 1. 2. 3. 4. 5. Holt Algebra 1

7 -4 Division Properties of Exponents Lesson Quiz: Part II Simplify. 6. Simplify (3

7 -4 Division Properties of Exponents Lesson Quiz: Part II Simplify. 6. Simplify (3 1012) ÷ (5 105) and write the answer in scientific notation. 6 106 7. The Republic of Botswana has an area of 6 105 square kilometers. Its population is about 1. 62 106. What is the population density of Botswana? Write your answer in standard form. 2. 7 people/km 2 Holt Algebra 1