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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.
Holt Algebra 1
7-4 Division Properties of Exponents
Use division properties of exponents to evaluate and simplify
expressions.
Objective
Holt Algebra 1
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
Simplify.
Example 1: Finding Quotients of Powers
A. B.
Holt Algebra 1
7-4 Division Properties of Exponents
C.
Simplify.
Example 1: Finding Quotients of Powers
D.
Holt Algebra 1
7-4 Division Properties of Exponents
Both and 729 are considered to be simplified.
Helpful Hint
Holt Algebra 1
7-4 Division Properties of Exponents
Check It Out! Example 1
a.
Simplify.
b.
Holt Algebra 1
7-4 Division Properties of Exponents
Check It Out! Example 1
Simplify.
c. d.
Holt Algebra 1
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
You can “split up” a quotient of products into a product of quotients:
Example:
Writing Math
Holt Algebra 1
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 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 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.
Simplify each quotient.
Simplify the exponent.
Write in standard form.
Holt Algebra 1
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 per person? Write your answer in standard form.
To find the average debt per 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
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
Simplify each quotient.
Simplify the exponent.
Write in standard form.
The average debt per person was $12,800.
Holt Algebra 1
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
Simplify.
Example 4A: Finding Positive Powers of Quotient
Use the Power of a Quotient Property.
Simplify.
Holt Algebra 1
7-4 Division Properties of Exponents
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:
Holt Algebra 1
7-4 Division Properties of Exponents
Simplify.
Example 4C: Finding Positive Powers of Quotient
Use the Power of a Product Property.
Use the Power of a Product Property:
Use the Power of a Product Property:
Holt Algebra 1
7-4 Division Properties of Exponents
Simplify.
Example 4C Continued
Use the Power of a Product Property:
Holt Algebra 1
7-4 Division Properties of Exponents
Check It Out! Example 4a
Simplify.
Use the Power of a Quotient Property.
Simplify.
Holt Algebra 1
7-4 Division Properties of Exponents
Check It Out! Example 4b
Simplify.
Holt Algebra 1
7-4 Division Properties of Exponents
Check It Out! Example 4c
Simplify.
Holt Algebra 1
7-4 Division Properties of Exponents
Therefore,
Write the fraction as division.
Use the Power of a Quotient Property.
Multiply by the reciprocal.
Simplify.
Use the Power of a Quotient Property.
Remember that What if x is a fraction?.
Holt Algebra 1
7-4 Division Properties of Exponents
Holt Algebra 1
7-4 Division Properties of Exponents
Simplify.
Example 5A: Finding Negative Powers of Quotients
Rewrite with a positive exponent.
and
Use the Powers of a Quotient Property .
Holt Algebra 1
7-4 Division Properties of Exponents
Simplify.
Example 5B: Finding Negative Powers of Quotients
Holt Algebra 1
7-4 Division Properties of Exponents
Simplify.
Example 5C: Finding Negative Powers of Quotients
Rewrite each fraction with a positive exponent.
Use the Power of a Quotient Property.
Use the Power of a Product Property:
(3)2 (2n)3 = 32 23n3
and (2)2 (6m)3 = 22 63m3
Holt Algebra 1
7-4 Division Properties of Exponents
1
241
21
12
Divide out common factors.
Simplify.
Example 5C: Finding Negative Powers of Quotients
Simplify.
Square and cube terms.
Holt Algebra 1
7-4 Division Properties of Exponents
Whenever all of the factors in the numerator or the denominator divide out, replace
them with 1.
Helpful Hint
Holt Algebra 1
7-4 Division Properties of Exponents
Check It Out! Example 5a
Simplify.
93=729 and 43 = 64.
Use the power of a Quotient Property.
Rewrite with a positive exponent.
Holt Algebra 1
7-4 Division Properties of Exponents
Check It Out! Example 5b
Simplify.
Rewrite with a positive exponent.
Use the Power of a Power Property: (b2c3)4=
b2•4c3•4 = b8c12 and (2a)4= 24a4= 16a4.
Use the Power of a Quotient Property.
Holt Algebra 1
7-4 Division Properties of Exponents
Check It Out! Example 5c
Simplify.
Rewrite each fraction with a positive exponent.
Use the Power of a Quotient Property.
Use the Power of a Product Property: (3)2= 9.
Add exponents and divide out common terms.
Holt Algebra 1
7-4 Division Properties of Exponents
Lesson Quiz: Part I
1.
3. 4.
5.
2.
Simplify.
Holt Algebra 1
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/km2
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