Transcript 2-7 - Kyrene School District

Page 734 and 735 ANSWERS
2-7 Properties of Exponents
Pre-Algebra
2-7 Properties of Exponents
Today’s Learning Goal Assignment
Learn to apply the
properties of
exponents and to
evaluate the zero
exponent.
Pre-Algebra
2-7 Properties of Exponents
Pre-Algebra
P. 86 #14-26 ANSWERS
P. 87 Spiral Review ANSWERS
ofofExponents
2-7
2-7 Properties
Properties
Exponents
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
Pre-Algebra
2-7 Properties of Exponents
Warm Up
Evaluate.
1. 33
27
2. 4 • 4 • 4 • 4
256
3. b2 for b = 4
16
4. n2r for n = 3 and r = 2
18
Pre-Algebra
2-7 Properties of Exponents
Problem of the Day
Calculate 6 to the fourth power minus 56.
1240
Pre-Algebra
2-7 Properties of Exponents
Today’s Learning Goal Assignment
Learn to apply the
properties of
exponents and to
evaluate the zero
exponent.
Pre-Algebra
2-7 Properties of Exponents
The factors of a power, such as 74, can be
grouped in different ways. Notice the
relationship of the exponents in each product.
7 • 7 • 7 • 7 = 74
(7 • 7 • 7) • 7 = 73 • 71 = 74
(7 • 7) • (7 • 7) = 72 • 72 = 74
Pre-Algebra
2-7 Properties of Exponents
MULTIPLYING POWERS WITH THE SAME BASE
Words
Numbers
To multiply
powers with
35 • 38 =
the same base, 5 + 8
3
= 313
keep the base
and add the
exponents.
Pre-Algebra
Algebra
bm • bn =
bm + n
2-7 Properties of Exponents
Additional Example 1A & 1B: Multiplying Powers with
the Same Base
Multiply. Write the product as one power.
A. 66 • 63
66 + 3
69
Add exponents.
B. n5 • n7
n5 + 7
n 12
Add exponents.
Pre-Algebra
2-7 Properties of Exponents
Additional Example 1: Multiplying Powers with the
Same Base Continued
Multiply. Write the product as one power.
C. 25 • 2
25 + 1
26
Think: 2 = 2 1
Add exponents.
D. 244 • 244
24 4 + 4
24 8
Pre-Algebra
Add exponents.
2-7 Properties of Exponents
Try This: Example 1A & 1B
Multiply. Write the product as one power.
A. 42 • 44
42 + 4
46
Add exponents.
B. x2 • x3
x2 + 3
x5
Add exponents.
Pre-Algebra
2-7 Properties of Exponents
Try This: Example 1C & 1D
Multiply. Write the product as one power.
C. x5 • y2
x5 • y2
Cannot combine; the bases are
not the same.
D. 412 • 417
41 2 + 7
41 9
Pre-Algebra
Add exponents.
2-7 Properties of Exponents
Notice what occurs when you divide powers
with the same base.
55555
55555
55
2
=
5
•
5
=
=
=
5
555
555
53
DIVIDING POWERS WITH THE SAME BASE
Words
To divide powers
with the same
base, keep the
base and subtract
the exponents.
Pre-Algebra
Numbers
6 9 = 69 – 4 = 6 5
64
Algebra
b m = bm – n
bn
2-7 Properties of Exponents
Additional Example 2: Dividing Powers with the Same
Base
Divide. Write the product as one power.
A.
5
7
3
7
75 – 3
7
Subtract exponents.
2
10
B. x9
x
x10 – 9
x
Pre-Algebra
Subtract exponents.
Think: x1 = x
2-7 Properties of Exponents
Try This: Example 2
Divide. Write the product as one power.
A.
99
92
99 – 2
97
B.
e 10
e5
e10 – 5
5
e
Pre-Algebra
Subtract exponents.
Subtract exponents.
2-7 Properties of Exponents
When the numerator and denominator have the
same base and exponent, subtracting the exponents
results in a 0 exponent.
2
4
2 – 2 = 40 = 1
=
1=
4
42
This result can be confirmed by writing out the factors.
42
42
Pre-Algebra
(4 • 4)
(4 • 4)
= 1 =1
=
=
(4 • 4)
1
(4 • 4)
2-7 Properties of Exponents
Helpful Hint
00 does not exist because 00 represents a
quotient of the form
0n .
0n
But the denominator of this quotient is 0,
which is impossible, since you cannot
divide by 0.
Pre-Algebra
2-7 Properties of Exponents
THE ZERO POWER
Words
Numbers
The zero power of
any number
except 0 equals 1.
1000 = 1
Pre-Algebra
(–7)0 = 1
Algebra
a = 1, if a  0
2-7 Properties of Exponents
Additional Example 3: Astronomy Application
A light-year, or the distance light travels
in one year, is almost 1018 centimeters.
To convert this number to kilometers,
you must divide by 105. How many
kilometers is a light-year?
10 18
10 5
10 18 - 5
Subtract exponents.
13
10
A light-year is almost 1013 km.
Pre-Algebra
2-7 Properties of Exponents
Try This: Example 3
A ship has 107 kilograms of grain loaded into
its cargo hold. A metric ton is 103 kilograms.
How many metric tons of grain were loaded?
10
103
7
The weight in metric tons is equal to
the weight in kilograms divided by
3
10 kilograms per metric ton.
107 - 3 Subtract exponents.
10 4
The ship had 104 metric tons of grain loaded.
Pre-Algebra
2-7 Properties of Exponents
Lesson Quiz: Part 1
Write the product or quotient as one power
1. n3  n4
n7
2. 8 • 88
89
109
3.
105
104
t9
4.
t7
t
2
5. 33 • 32 • 35
Pre-Algebra
310
2-7 Properties of Exponents
Lesson Quiz: Part 2
6. A school would like to purchase new
globes. They can get six dozen for
$705.80 from Company A. From
Company B, they can buy a half gross
for $725.10. Which company should
they buy from? (1 gross = 122 items)
Company A
Pre-Algebra