7.4 division properties of exponents algebra 7.4
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7 .4 DIVISION PROPERTIES OF EXPONENTS
Algebra 7.4
Learning Targets 7.4
Language GoalStudents should be able to read, write, and
say expressions with exponents.Math GoalStudents should be able to use division
properties of exponents to evaluate and simplify expressions.
Essential QuestionWhy is it important to have properties to
simplify expressions?
Warm-up
Homework Check
Quotient of Powers Property
The quotient of two nonzero powers with the same base equals the base raised to the difference of the exponents.
67
64=67−4=63 𝑎𝑥
𝑎𝑦 =𝑎𝑥−𝑦
Example 1: Finding Quotients of Powers
A. B.
C. D.
Example 1: Finding Quotients of Powers
Your Turn!E. F.
Example Type 2: Dividing Numbers in Scientific Notation
A. Simplify 8) and write the answer in scientific notation.
Example Type 2: Dividing Numbers in Scientific Notation
B. Simplify and write the answer in scientific notation.
Example Type 2: Dividing Numbers in Scientific Notation
C. Simplify and write the answer in scientific notation.
Example Type 3: Word Problems
A. In the year 2000, the United States public debt was about 5.6 x dollars. The population of the United States in that year was about 2.8 x people. What was the average debt per person Give your answer in standard form.
Example Type 3: Word Problems
B. In 1990, The United States Public debt was about 3.2 x dollars. The population of the United States in 1990 was about 2.5 x people. What was the average debt per person Write your answer in standard form.
Positive Power of a Quotient Property
The quotient raised to a positive power equals the quotient of each base raised to that power.
( 35 )4
=35∙35∙35∙35=3
4
54 (𝑎𝑏 )𝑛
= 𝑎𝑛
𝑏𝑛
Example Type 4: Finding Positive Powers of Quotients
SimplifyA. B. C.
Example Type 4: Finding Positive Powers of Quotients
SimplifyD. E.
Negative Power of a Quotient Property
Remember What if x is a fraction?
A quotient raised to a negative power equals the reciprocal of the quotient raised to the
opposite (positive) power.
(𝑎𝑏 )−𝑛
=(𝑏𝑎 )𝑛
=𝑏𝑛
𝑎𝑛( 23 )−4
=( 32 )4
=34
24
Example Type 5: Finding Negative Powers of Quotients
SimplifyA. B. C.
Example Type 5: Finding Negative Powers of Quotients
SimplifyD. E.
7.4 Extra Practice
7.4 Extra Practice
Lesson Quiz
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