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