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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8.5
Dividing Exponents
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Warm UpSimplify.
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.
8.5 – Dividing Exponents
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8.5 – Dividing Exponents
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8.5 – Dividing Exponents
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
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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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Check It Out! Example 1
a.
Simplify.
b.
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Check It Out! Example 1
Simplify.
c. d.
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8.5 – Dividing Exponents
Simplify:
aa
6
14
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8.5 – Dividing Exponents
Simplify:
c dc d
-1
5
3
- 4
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8.5 – Dividing Exponents
Simplify:
bb
4
9
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8.5 – Dividing Exponents
Simplify:
zz
10
5
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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.
Simplify the exponent.
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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.
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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.
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8.5 – Dividing Exponents
What happens if we have an expression like this?
24x( )
3
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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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8.5 – Dividing Exponents
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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.
Use the Power of a Product Property:
Use the Power of a Product Property:
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Simplify.
Example 4C Continued
Use the Power of a Product Property:
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Check It Out! Example 4a
Simplify.
Use the Power of a Quotient Property.
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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8.5 – Dividing Exponents
Simplify
23x( )
2
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8.5 – Dividing Exponents
Simplify
2xy( )
3
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8.5 – Dividing Exponents
Simplify
35( )
- 2
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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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Lesson Quiz: Part I
1.
3. 4.
5.
2.
Simplify.
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