Transcript Document

Properties of
Exponents
Learn to apply the properties of exponents
and to evaluate the zero exponent.
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
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.
Algebra
bm • bn =
bm + n
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
n12
Add exponents.
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
Add 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.
Numbers
6 9 = 69 – 4 = 6 5
64
Algebra
b m = bm – n
bn
Dividing Powers with the Same Base
Divide. Write the quotient as one power.
A.
5
7
3
7
75 – 3
7
Subtract exponents.
2
10
B. x9
x
x10 – 9
x
Subtract exponents.
Think: x1 = x
Try This:
Divide. Write the quotient as one power.
A.
99
92
99 – 2
97
B.
Subtract exponents.
e 10
e5
e10 – 5
5
e
Subtract 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
(4 • 4)
(4 • 4)
= 1 =1
=
=
(4 • 4)
1
(4 • 4)
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! It is undefined!
THE ZERO POWER
Words
Numbers
The zero power
of any number
except 0 equals 1.
1000 = 1
(–7)0 = 1
Algebra
a = 1, if a  0
Practice
Write the product or quotient as one power
1. n3  n4
2.
109
105
9
t
3.
t7
4. 33 • 32 • 35
5. 8 • 88 =
1. n7
2. 104
3. t2
4. 310
5. 89