8.5 dividing exponents. warm up simplify. 1. (x 2 ) 3 3. 5. 2.2. 4. 6. 7. write in scientific...

8.5

Dividing Exponents

Warm UpSimplify.

1. (x2)3

3.

5.

2.

4.

6.

7.

Write in Scientific Notation.

8.

8.5 – Dividing Exponents

Use division properties of exponents to evaluate and simplify expressions.

Objective


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.



When we multiply exponents with the same base ADDADD the exponents!

When we divide exponents with the same base SUBTRACTSUBTRACT the exponents!!!

55

6

2 = 56 - 2

= 54

54

54

* = 54 + 4

= 58

Simplify.Example 1: Finding Quotients of Powers

A. B.


C.

Simplify.Example 1: Finding Quotients of Powers

D.


Check It Out! Example 1

a.

Simplify.

b.


Check It Out! Example 1

Simplify.

c. d.



Simplify:

aa

6

14


Simplify:

c dc d

-1

5

3

- 4


Simplify:

bb

4

9


Simplify:

zz

10

5

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.


Example 3: Application

The Michigan Department of Education spent about dollars in fiscal year 2010-11 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.


Example 3 Continued

The Michigan Department of Education spent about dollars in fiscal year 2010-11 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.



What happens if we have an expression like this?

24x( )

3

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.


Simplify.

Example 4A: Finding Positive Powers of Quotient

Use the Power of a Quotient Property.

Simplify.


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:


Simplify.

Example 4C: Finding Positive Powers of Quotient

Use the Power of a Product Property.




Simplify.

Example 4C Continued



Check It Out! Example 4a

Simplify.

Use the Power of a Quotient Property.

Simplify.


Check It Out! Example 4b Simplify.


Check It Out! Example 4c Simplify.



Simplify

23x( )

2


Simplify

2xy( )

3


Simplify

35( )

- 2

Simplify.

Example 5A: Finding Negative Powers of Quotients

Rewrite with a positive exponent.

and

Use the Powers of a Quotient Property .


Simplify.

Example 5B: Finding Negative Powers of Quotients


Lesson Quiz: Part I

1.

3. 4.

5.

2.

Simplify.


8.5 dividing exponents. warm up simplify. 1. (x 2 ) 3 3. 5. 2.2. 4. 6. 7. write in scientific...

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