Laws of Exponents

Pre-Algebra
2-7 Properties of Exponents2-7 Properties of Exponents
Pre-Algebra
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation

Pre-Algebra
2-7 Properties of Exponents
Warm Up
Evaluate.
Pre-Algebra
271. 33
2. 4 • 4 • 4 • 4
3. b2
for b = 4
4. n2
r for n = 3 and r = 2
256
16
18

Pre-Algebra
Problem of the Day
Calculate 6 to the fourth power minus 56.

Pre-Algebra
Learn to apply the properties of exponents
and to evaluate the zero exponent.

Pre-Algebra
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
Words Numbers Algebra
To multiply
powers with
the same base,
keep the base
and add the
exponents.
bm
• bn
=
bm + n
35
• 38
=
35 + 8
= 313
MULTIPLYING POWERS WITH THE SAME BASE

Pre-Algebra
Additional Example 1A & 1B: Multiplying Powers with
the Same Base
A. 66
• 63
69
66 + 3
B. n5
• n7
n12
n5 + 7
Add exponents.
Add exponents.
Multiply. Write the product as one power.

Pre-Algebra
D. 244
• 244
C. 25
• 2
26
25 + 1
248
244 + 4
Think: 2 = 21
Additional Example 1: Multiplying Powers with the
Same Base Continued
Add exponents.
Add exponents.

Pre-Algebra
Try This: Example 1A & 1B
A. 42
• 44
46
42 + 4
B. x2
• x3
x5
x2 + 3
Add exponents.
Add exponents.

Pre-Algebra
D. 412
• 417
C. x5
• y2
419
412 + 7
Try This: Example 1C & 1D
Cannot combine; the bases are
not the same.
Add exponents.
x5
• y2

Pre-Algebra
Notice what occurs when you divide powers
with the same base.
DIVIDING POWERS WITH THE SAME BASE
To divide powers
with the same
base, keep the
base and subtract
the exponents.
6569 – 469
64
= = bm – nbm
bn
=
55
53
=
5 • 5 • 5
5 • 5 • 5 • 5 • 5
= 5 • 5 = 52=
5 • 5 • 5
5 • 5 • 5 • 5 • 5

Pre-Algebra
Subtract exponents.
7
2
75 – 3
7
5
7
3
Additional Example 2: Dividing Powers with the Same
Base
Divide. Write the product as one power.
A.
x
10
x
9
B.
Subtract exponents.x10 – 9
x Think: x = x1

Pre-Algebra
Subtract exponents.
97
99 – 2
99
92
Try This: Example 2
Divide. Write the product as one power.
A.
B.
e10
e5
Subtract exponents.e10 – 5
e
5

Pre-Algebra
When the numerator and denominator have the
same base and exponent, subtracting the exponents
results in a 0 exponent.
This result can be confirmed by writing out the factors.
1 = 42
42 42 – 2
= 40
= 1=
=
(4 • 4)
(4 • 4)
= 11
1
=42
2
=
(4 • 4)
4 (4 • 4)

Pre-Algebra
0
0 does not exist because 00
represents a
quotient of the form
But the denominator of this quotient is 0,
which is impossible, since you cannot
divide by 0.
Helpful Hint
0n
0n
.

Pre-Algebra
THE ZERO POWER
The zero power of
any number
except 0 equals 1.
1000
= 1
(–7)0
= 1
a0
= 1, if a ≠ 0

Pre-Algebra
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 - 5
A light-year is almost 1013
km.
10
13
10 18
10 5
Subtract exponents.
Additional Example 3: Astronomy Application

Pre-Algebra
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?
107 - 3
The ship had 104
metric tons of grain loaded.
104
107
103
Subtract exponents.
The weight in metric tons is equal to
the weight in kilograms divided by
10 kilograms per metric ton.
3
Try This: Example 3

Pre-Algebra
Lesson Quiz: Part 1
Write the product or quotient as one power
3.
89
n 71. n3
× n4
109
105
104
4. t 2
5. 33
• 32
• 35
310
2. 8 • 88
t9
t7

Pre-Algebra
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)
Lesson Quiz: Part 2
Company A
6.

Laws of Exponents

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