Holt Algebra 1 7-4 Division Properties of Exponents 7-4 Division Properties of Exponents Holt Algebra 1 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson

Holt Algebra 1

7-4 Division Properties of Exponents7-4 Division Properties of Exponents

Holt Algebra 1

Warm Up

Lesson Quiz

Lesson Presentation

Holt Algebra 1

7-4 Division Properties of Exponents

Warm Up

Simplify.

1. (x2)3

3.

5.

2.

4.

6.

7.

Write in Scientific Notation.

8.

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Use division properties of exponents to evaluate and simplify

expressions.

Objective

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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.

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Holt Algebra 1


Simplify.

Example 1: Finding Quotients of Powers

A. B.

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C.

Simplify.

Example 1: Finding Quotients of Powers

D.

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Both and 729 are considered to be simplified.

Helpful Hint

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Check It Out! Example 1

a.

Simplify.

b.

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Simplify.

c. d.

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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.


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You can “split up” a quotient of products into a product of quotients:

Example:

Writing Math

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Simplify and write the answer in scientific notation.




Write 1.1 in scientific notation as 11 x 10 .

The second two terms have the same base, so add

the exponents.


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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.


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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.

The average spending per student is $5,800.



Write in standard form.

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In 1990, the United States public debt was about dollars. The

population of the United States was about people. What was the

average debt per person? Write your answer in standard form.

To find the average debt per person, divide the total debt by the number of people.


Holt Algebra 1


In 1990, the United States public debt was about dollars. The

population of the United States was about people. What was the

average debt per person? Write your answer in standard form.

To find the average debt per person, divide the total debt by the number of people.

Check It Out! Example 3 Continued



Write in standard form.

The average debt per person was $12,800.

Holt Algebra 1


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.

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Holt Algebra 1


Simplify.

Example 4A: Finding Positive Powers of Quotient

Use the Power of a Quotient Property.

Simplify.

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Simplify.

Example 4B: Finding Positive Powers of Quotient

Use the Power of a Product Property.

Use the Power of a Product Property:

Simplify and use the Power of a Power Property:

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Simplify.

Example 4C: Finding Positive Powers of Quotient

Use the Power of a Product Property.



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Simplify.

Example 4C Continued


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Check It Out! Example 4a

Simplify.


Simplify.

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Check It Out! Example 4b

Simplify.

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Check It Out! Example 4c

Simplify.

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Therefore,

Write the fraction as division.


Multiply by the reciprocal.

Simplify.


Remember that What if x is a fraction?.

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Holt Algebra 1


Simplify.

Example 5A: Finding Negative Powers of Quotients

Rewrite with a positive exponent.

and

Use the Powers of a Quotient Property .

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Simplify.

Example 5B: Finding Negative Powers of Quotients

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Simplify.

Example 5C: Finding Negative Powers of Quotients

Rewrite each fraction with a positive exponent.



(3)2 (2n)3 = 32 23n3

and (2)2 (6m)3 = 22 63m3

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1

241

21

12

Divide out common factors.

Simplify.

Example 5C: Finding Negative Powers of Quotients

Simplify.

Square and cube terms.

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Whenever all of the factors in the numerator or the denominator divide out, replace

them with 1.

Helpful Hint

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Check It Out! Example 5a

Simplify.

93=729 and 43 = 64.

Use the power of a Quotient Property.


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Check It Out! Example 5b

Simplify.


Use the Power of a Power Property: (b2c3)4=

b2•4c3•4 = b8c12 and (2a)4= 24a4= 16a4.


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Check It Out! Example 5c

Simplify.

Rewrite each fraction with a positive exponent.


Use the Power of a Product Property: (3)2= 9.

Add exponents and divide out common terms.

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Lesson Quiz: Part I

1.

3. 4.

5.

2.

Simplify.

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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/km2

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Holt Algebra 1 7-4 Division Properties of Exponents 7-4 Division Properties of Exponents Holt Algebra 1 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson