Download 8.5 – Dividing Exponents

8.5 – Dividing Exponents
Warm Up
Simplify.
1. (x2)3
2.
3.
4.
5.
6.
Write in Scientific Notation.
7.
8.
Lesson #8.5
Division Properties
of Exponents
Objective:
SWBAT divide powers with the same base and
raise a quotient to a power.
8.5 – Dividing Exponents
Objective
Use division properties of exponents to
evaluate and simplify expressions.
8.5 – Dividing 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.
8.5 – Dividing Exponents
8.5 – Dividing Exponents

When we multiply exponents with the same
base ADD the exponents!
4
5 * 5

4
= 5
4+4
= 5
8
When we divide exponents with the same
base SUBTRACT the exponents!!!
6
5 =
2
5
5
6-2
= 5
4
8.5 – Dividing Exponents
Example 1: Finding Quotients of Powers
Simplify.
A.
B.
8.5 – Dividing Exponents
Example 1: Finding Quotients of Powers
Simplify.
C.
D.
8.5 – Dividing Exponents
Check It Out! Example 1
Simplify.
a.
b.
8.5 – Dividing Exponents
Check It Out! Example 1
Simplify.
c.
d.
8.5 – Dividing Exponents

Simplify:
6
a
14
a
8.5 – Dividing Exponents

Simplify:
-1
3
c d
5 -4
c d
8.5 – Dividing Exponents

Simplify:
4
b
9
b
8.5 – Dividing Exponents

Simplify:
10
z
5
z
8.5 – Dividing 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.
8.5 – Dividing Exponents
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.
8.5 – Dividing Exponents
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.
Simplify each quotient.
Simplify the exponent.
Write in standard form.
The average spending per student is $5,800.
8.5 – Dividing Exponents

What happens if we have an expression like
this?
4
2
x
3
( )
8.5 – Dividing 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.
8.5 – Dividing Exponents
8.5 – Dividing Exponents
Example 4A: Finding Positive Powers of Quotient
Simplify.
Use the Power of a Quotient
Property.
Simplify.
8.5 – Dividing Exponents
Example 4B: Finding Positive Powers of Quotient
Simplify.
Use the Power of a Product
Property.
Use the Power of a Product
Property:
Simplify and use the Power
of a Power Property:
8.5 – Dividing Exponents
Example 4C: Finding Positive Powers of Quotient
Simplify.
Use the Power of a Product
Property.
Use the Power of a Product
Property:
Use the Power of a Product
Property:
8.5 – Dividing Exponents
Example 4C Continued
Simplify.
Use the Power of a Product
Property:
8.5 – Dividing Exponents
Check It Out! Example 4a
Simplify.
Use the Power of a Quotient
Property.
Simplify.
8.5 – Dividing Exponents
Simplify.
Check It Out! Example 4b
8.5 – Dividing Exponents
Simplify.
Check It Out! Example 4c
8.5 – Dividing Exponents

Simplify
3
2
x
2
( )
8.5 – Dividing Exponents

Simplify
x
2
y
3
( )
8.5 – Dividing Exponents

Simplify
3
5
-2
( )
8.5 – Dividing Exponents
Example 5A: Finding Negative Powers of Quotients
Simplify.
Rewrite with a positive exponent.
Use the Powers of a Quotient
Property .
and
8.5 – Dividing Exponents
Example 5B: Finding Negative Powers of Quotients
Simplify.
8.5 – Dividing Exponents
Lesson Quiz: Part I
Simplify.
1.
2.
3.
4.
5.