Download Chapter 7-2 handout from the Algebra book ANSWERS

NAME
DATE
7-2
PERIOD
Study Guide and Intervention
Division Properties of Exponents
Divide Monomials
To divide two powers with the same base, subtract the
exponents.
Quotient of Powers
am
m-n
.
For all integers m and n and any nonzero number a, −
n = a
Power of a Quotient
a
For any integer m and any real numbers a and b, b ≠ 0, −
a
(b)
a 4b 7
Simplify −
. Assume
2
Example 2
ab
that no denominator equals zero.
( )( )
a 4b 7
a4 b7
−
= −
2
a −
ab
b2
4-1
7-2
= (a )(b )
= a3b5
The quotient is a3b5.
am
=−
m .
b
3
2a 3b 5
Simplify −
. Assume
2
( 3b )
that no denominator equals zero.
Group powers with the same base.
3
5
2
Quotient of Powers
Simplify.
3
(2a 3b 5) 3
(3b )
2 3(a 3) 3(b 5) 3
=−
(3) 3(b 2) 3
8a 9b 15
=−
27b 6
8a 9b 9
=−
27
8a 9b 9
The quotient is −
.
27
2a b
(−
3b )
=−
2 3
Power of a Quotient
Power of a Product
Power of a Power
Quotient of Powers
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exercises
Simplify each expression. Assume that no denominator equals zero.
55 3
5 or 125
1. −
2
5
m6
2. −
m2
4
a2
4. −
a a
5. −
y
5 2
xy 6
yx
(rw )
2r 5w 3
10. −
4 3
Chapter 7
m
x 5y 3
xy
6. −5 - −y 2
(
)
2a 2b
8. −
a
y2
7. −
4
4
16r 4
p 5n 4
pn
3. −
p3n3
2
3
( 2r n )
3r 6n 3
11. −
5
4
-2y 7
14y
8a3b3
81
16
− r 4n 8
11
( )
4p 4r 4
3p r
9. −
2 2
1
7
3
64
27
− p 6r 6
r 7n 7t 2 4 4
12. −
rn
3 3 2
nrt
Glencoe Algebra 1
Lesson 7-2
Example 1
m
NAME
DATE
7-2
Study Guide and Intervention
PERIOD
(continued)
Division Properties of Exponents
Negative Exponents
Any nonzero number raised to the zero power is 1; for example,
(-0.5)0 = 1. Any nonzero number raised to a negative power is equal to the reciprocal of the
1
. These definitions can be used to
number raised to the opposite power; for example, 6 -3 = −
3
6
simplify expressions that have negative exponents.
Zero Exponent
For any nonzero number a, a0 = 1.
Negative Exponent Property
1
1
n
For any nonzero number a and any integer n, a -n = −
n and −
-n = a .
a
a
The simplified form of an expression containing negative exponents must contain only
positive exponents.
-3
6
4a b
. Assume that no denominator equals zero.
Simplify −
2 6 -5
Example
16a b c
-3
( 16 )( a )( b )( c )
6
-3
6
4a b
b
4 a
1
−
−
−
−
= −
2 6 -5
2
6
-5
16a b c
1
=−
(a -3-2)(b 6-6)(c 5)
( )
Quotient of Powers and Negative Exponent Properties
Simplify.
Negative Exponent and Zero Exponent Properties
Simplify.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4
1 -5 0 5
=−
a bc
4
1 1
− (1)c 5
=−
4 a5
c5
=−
4a 5
c5
The solution is −
.
4a 5
Group powers with the same base.
Exercises
Simplify each expression. Assume that no denominator equals zero.
p -8 1
p p
22
25 or 32
1. −
-3
m
2. −
m5
-4
b -4
b
4. −
-5
b
−2
5. −
-1 2
x 4y 0
x
−
8. −
2 4
2 6
2
7. −
x6
-2
1
m -3t -5
−2
10. −
2 3 -1
(m t )
Chapter 7
mt
−
3. −
3
11
m
(-x -1y) 0 w
4w y
4y
6. −
a6 b8
-2
(6a -1b) 2 36
(b )
ab
−
9. −
-1 2 7
11
( 8m )
4m 2n 2
11. −
-1
0
1
12
(a 2b 3) 2
(ab)
(3rt) 2u -4 9r 3
r tu
u
(-2mn 2) -3
4m n
m3
32n
12. −
-−
-6 4
10
Glencoe Algebra 1