Algebra Exponents Practice
-
Upload
kking-chung -
Category
Documents
-
view
219 -
download
0
Transcript of Algebra Exponents Practice
-
7/21/2019 Algebra Exponents Practice
1/30Math-Aids.Com
Exponent PropertiesExponent Properties
1. Zero Exponent:
Any number raised to the zero power is equal to 1, except for zero which is not defined.
a
0
= 1 ; a /=0 where as 0
0
is not defined
Example: 40= 1 and 2500
0= 1
2. Negative Exponent:
Negative exponents indicate reciprocation, with the exponent of the reciprocal becoming positiv
a-n=
1
an
__ or1
a-n
__ = an; a /
=0
Example: 3-2=
1
32
__ or1
4-3
__ = 43 or
1
n-1
__ = n
3. Product of like bases:
To multiply powers with the same base, add the exponents and keep the common base.
am
an
= am+n
; a /=0
Example: 232
2= 2
5= 32
4. Quotient of like bases:
To divide powers with the same base, subtract the exponents and keep the common base.
am
an
__
= a
m-n
; a /=0
Example:3
5
33
__ = 35-3
= 32
-
7/21/2019 Algebra Exponents Practice
2/30Math-Aids.Com
Exponent PropertiesExponent Properties
5. Power to a power:
To raise a power to a power, keep the base and multiply the exponents.
(a
m
)
n
= a
mn
Example: (22)
3
= 22x3
= 26
6. Product to a power:
To raise a product to a power, raise each factor to the power.
(ab)m = a
mb
m ; a /=0 and b /=0
Example: (2x3)2 = 2
2x 3
2
7. Quotient to a power:
To raise a quotient to a power, raise the numerator and the denominator to the power.
(ab
_ )n
=a
n
bn
__ ; a /=0 and b /=0
Example: (23
_ )2
=2
2
32
__
8. Rational Exponent:
The denominator of the rational exponent becomes the index of the radical,
and the numerator becomes the exponent of the radicand.
(a)xy_ = y ; a /=0ax
Example: (2)23_
=3
22
-
7/21/2019 Algebra Exponents Practice
3/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Exponents and DivisionExponents and Division
Simplify. Your answer should contain only positive exponents.
1)9z
-2
2z
___
2)7y
4y2
__
3)4cs
-4
3c-3s
4
____
4)7k2b5
5k4b
6
____
5)4z
6
2z
__
6)rh
3r5h
4
____
7)yw
2y-4w
-6
_____
8)2
-6
2
__
9)2y
-6c
-2
8yc-3
_____
10)d5
d-5
__
11)9r
4
4r3
__
12)9dg
6
8d4g
5
____
-
7/21/2019 Algebra Exponents Practice
4/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Exponents and DivisionExponents and Division
Simplify. Your answer should contain only positive exponents.
1)9z
-2
2z
___
9
2z3
__
2)7y
4y2
__
7
4y
__
3)4cs
-4
3c-3s
4
____
4c4
3s8
__
4)7k2b5
5k4b
6
____
7
5k2b
___
5)4z
6
2z
__
2z5
6)rh
3r5h
4
____
1
3r4h
3
____
7)yw
2y-4w
-6
_____
y5w
7
2
___
8)2
-6
2
__
1
27
__
9)2y
-6c
-2
8yc-3
_____
c
4y7
__
10)d5
d-5
__
d10
11)9r
4
4r3
__
9r4
__
12)9dg
6
8d4g
5
____
9g
8d3
___
-
7/21/2019 Algebra Exponents Practice
5/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Exponents and DivisionExponents and Division
Simplify. Your answer should contain only positive exponents.
1)3d
4
9d6
___
2)3h
-2
7h2
___
3)3
2
3
__
4)8dn-5
9d-3n
6
____
5)8w
-5
5w3b
-3
_____
6)8db
6
7d5b
3
____
7)5s
-2
8s-3
___
8)r
4
r-4
_
9)zb
5z6b
2
____
10)9g5
3g
___
11)2y
-4
7y
___
12)4w
-5h
5
5w2h
-2
_____
-
7/21/2019 Algebra Exponents Practice
6/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Exponents and DivisionExponents and Division
Simplify. Your answer should contain only positive exponents.
1)3d
4
9d6
___
1
3d2
___
2)3h
-2
7h2
___
3
7h4
___
3)3
2
3
__
3
4)8dn-5
9d-3n
6
____
8d4
9n11
___
5)8w
-5
5w3b
-3
_____
8b
3
5w8
___
6)8db
6
7d5b
3
____
8b3
7d4
___
7)5s
-2
8s-3
___
5s
8
__
8)r
4
r-4
_
r8
9)zb
5z6b
2
____
1
5z5b
___
10)9g5
3g
___
3g4
11)2y
-4
7y
___
27y
5__
12)4w
-5h
5
5w2h
-2
_____
4h7
5w7
___
-
7/21/2019 Algebra Exponents Practice
7/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Exponents with Multiplication and DivisionExponents with Multiplication and Division
Simplify. Your answer should contain only positive exponents.
1)6y
5y-5
___
2) 2r2 5r
4
3) nc 4n6c
3
4) 8-3 8
5
5)8ng
4
2n5g
2
____
6) (23
_ )5
(23
_ )3
(23
_ )4
7) 5h 4h-4
8) 6w-4r
4 9wr
-3
9)6h
3r
2
5hr5
____
10)kc
7k3c
4
____
11)7g
-4
3g5
___
12)k
4
k-4
__
-
7/21/2019 Algebra Exponents Practice
8/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Exponents with Multiplication and DivisionExponents with Multiplication and Division
Simplify. Your answer should contain only positive exponents.
1)6y
5y-5
___
6y6
5
__
2) 2r2 5r
4
10r6
3) nc 4n6c
3
4n7c
4
4) 8-3 8
5
82
5)8ng
4
2n5g
2
____
4g
2
n4
___
6) (23
_ )5
(23
_ )3
(23
_ )4
(23
_ )12
7) 5h 4h-4
20
h3
__
8) 6w-4r
4 9wr
-3
54 r
w3
__
9)6h
3r
2
5hr5
____
6h2
5r3
___
10)kc
7k3c
4
____
1
7k2c
3
____
11)7g
-4
3g5
___
73g
9___
12)k
4
k-4
__
k8
-
7/21/2019 Algebra Exponents Practice
9/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Exponents with Multiplication and DivisionExponents with Multiplication and Division
Simplify. Your answer should contain only positive exponents.
1)g
2
g-5
__
2) 5c 3c-5
3)2h
5h-4
___
4) (19
_ )2
(19
_ )5
5)5w
3
7w6
___
6)2
5
2
__
7)8w
5
4w
___
8) (14
_ )4
(14
_ )5
(14
_ )3
9) (35
_ )2
(35
_ )6
10) 4cg-2 7c
-4g
5
11)5b
-6w
-4
8bw-2
_____
12) dh 3d-2h
-3
-
7/21/2019 Algebra Exponents Practice
10/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Exponents with Multiplication and DivisionExponents with Multiplication and Division
Simplify. Your answer should contain only positive exponents.
1)g
2
g-5
__
g7
2) 5c 3c-5
15
c4
__
3)2h
5h-4
___
2h5
5
___
4) (19
_ )2
(19
_ )5
(19
_ )7
5)5w
3
7w6
___
57w
3___
6)2
5
2
__
24
7)8w
5
4w
___
2w4
8) (14
_ )4
(14
_ )5
(14
_ )3
(14
_ )12
9) (35
_ )2
(35
_ )6
(35
_ )8
10) 4cg-2 7c
-4g
5
28g
3
c3
__
11)5b
-6w
-4
8bw-2
_____
58b
7w
2____
12) dh 3d-2h
-3
3
dh2
___
-
7/21/2019 Algebra Exponents Practice
11/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Exponents and MultiplicationExponents and Multiplication
Simplify. Your answer should contain only positive exponents.
1) 4yk2 5y
3k
6
2) 5w5 2w
2 9w
3
3) 2 2-4
4) 86 8
4
5) d5 d
-6 d
-2
6) 7d 2d-4
7) 7g 6g-3
8) (49
_ )3
(49
_ )6
(49
_ )5
9) d3n
-6 9d
-4n
4 8dn
6
10) 4s2 2s
3
11) 6c 3c4
12) kd 2k2d
4
13) 8y2 2y
-6b
6
14) 3g5 7g
-2
-
7/21/2019 Algebra Exponents Practice
12/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Exponents and MultiplicationExponents and Multiplication
Simplify. Your answer should contain only positive exponents.
1) 4yk2 5y
3k
6
20y4k
8
2) 5w5 2w
2 9w
3
90w10
3) 2 2-4
1
23
__
4) 86 8
4
810
5) d5 d
-6 d
-2
1
d3
__
6) 7d 2d-4
14
d3
__
7) 7g 6g-3
42
g2
__
8) (49
_ )3
(49
_ )6
(49
_ )5
(49
_ )14
9) d3n
-6 9d
-4n
4 8dn
6
72 n4
10) 4s2 2s
3
8s5
11) 6c 3c4
18c5
12) kd 2k2d
4
2k3d
5
13) 8y2 2y
-6b
6
16b6
y4
____
14) 3g5 7g
-2
21g3
-
7/21/2019 Algebra Exponents Practice
13/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Exponents and MultiplicationExponents and Multiplication
Simplify. Your answer should contain only positive exponents.
1) 8d5b
3 7d
2b
4
2) 3k2n
-5 7k
-4n
4
3) 5d5 6d
-6k
4
4) (1b
_ )4
(1b
_ )5
(1b
_ )3
5) h-4 h
5
6) 2gs3 6g
2s
4
7) 5 54
8) (17
_ )3
(17
_ )6
(17
_ )4
9) 4r2 2r
-6
10) 6-4 6
5
11) z3 z
2 z
5
12) zd 4z-5d
-3
13) k6 k
-3 k
-5
14) 5d 6d3
-
7/21/2019 Algebra Exponents Practice
14/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Exponents and MultiplicationExponents and Multiplication
Simplify. Your answer should contain only positive exponents.
1) 8d5b
3 7d
2b
4
56d7b
7
2) 3k2n
-5 7k
-4n
4
21
k2
n
__
3) 5d5 6d
-6k
4
30k4
d
___
4) (1b
_ )4
(1b
_ )5
(1b
_ )3
(1b_ )12
5) h-4 h
5
h
6) 2gs3 6g
2s
4
12g3s
7
7) 5 54
55
8) (17
_ )3
(17
_ )6
(17
_ )4
(17
_ )13
9) 4r2 2r
-6
8
r4
_
10) 6-4 6
5
6
11) z3 z
2 z
5
z10
12) zd 4z-5d
-3
4
z4d
2
___
13) k6 k
-3 k
-5
1
k2
_
14) 5d 6d3
30d4
-
7/21/2019 Algebra Exponents Practice
15/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Operations with ExponentsOperations with Exponents
Simplify the exponents.
1) (3d2 d3 4d )3
2)6w
-3
7w2
___
3) (g 3g3)3
4)4gy5
8g6y
2
____
5)9
6
95
__
6) (5h
2
8h
___ )2
7) 8s6 6s
2 9s
3
8) (9d
2
8d5
___ )3
9) (1d
_ )2
(1d
_ )3
(1d
_ )4
10) (2s 4s3)2
11) 4n5r
-4 3n
-3r
4
12) (2bc
3
6b4c
6
____ )3
-
7/21/2019 Algebra Exponents Practice
16/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Operations with ExponentsOperations with Exponents
Simplify the exponents.
1) (3d2 d3 4d )3
1728d18
2)6w
-3
7w2
___
6
7w5
___
3) (g 3g3)3
27g12
4)4gy5
8g6y
2
____
y3
2g5
___
5)9
6
95
__
9
6) (5h
2
8h
___ )2
25h2
64
____
7) 8s6 6s
2 9s
3
432s11
8) (9d
2
8d5
___ )3
729
512d9
_____
9) (1d
_ )2
(1d
_ )3
(1d
_ )4
(1d
_ )9
10) (2s 4s3)2
64s8
11) 4n5r
-4 3n
-3r
4
12n2
12) (2bc
3
6b4c
6
____ )3
1
27b9c
9
_____
-
7/21/2019 Algebra Exponents Practice
17/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Operations with ExponentsOperations with Exponents
Simplify the exponents.
1) h-6 h
3
2) (2k
3
7k4y
5
____ )2
3)5z
4r
5
8z2r
3
____
4) 6b3k
5 8bk
2
5) (6sr6)6
6) (7h6b )3
7) (8
6
8
__ )3
8)2c
-6g
-3
6cg-4
_____
9) (9d
5
7d6
___ )3
10) (13
_ )6
(13
_ )3
(13
_ )2
11)6k
3
3k5
__
12) (s 4s2 s3)3
-
7/21/2019 Algebra Exponents Practice
18/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Operations with ExponentsOperations with Exponents
Simplify the exponents.
1) h-6 h
3
1
h3
__
2) (2k
3
7k4y
5
____ )2
4
49k2y
10
_____
3)5z
4r
5
8z2r
3
____
5z2r
2
8
____
4) 6b3k
5 8bk
2
48b4k
7
5) (6sr6)6
46656s6r36
6) (7h6b )3
343h18
b3
7) (8
6
8
__ )3
815
8)2c
-6g
-3
6cg-4
_____
g
3c7
__
9) (9d
5
7d6
___ )3
729
343d3
_____
10) (13
_ )6
(13
_ )3
(13
_ )2
(13
_ )11
11)6k
3
3k5
__
2k
2_
12) (s 4s2 s3)3
64s18
-
7/21/2019 Algebra Exponents Practice
19/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Powers of ProductsPowers of Products
Simplify the exponents.
1) (3d 2d2)2
2) (3n2 n )2
3) (2r3 3r )2
4) (2s2 3s3)2
5) (8d4)2
6) (d 3d2)3
7) (3s2 s 2 )3
8) (3c4g )4
9) (3n3 4n n2)3
10) (2b2 b2)3
11) (z 2z2 z3)3
12) (6ky5)3
13) (2h2 3h3 h )2
14) (3n2 n3 4n )2
-
7/21/2019 Algebra Exponents Practice
20/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Powers of ProductsPowers of Products
Simplify the exponents.
1) (3d 2d2)2
36d6
2) (3n2 n )2
9n6
3) (2r3 3r )2
36r8
4) (2s2 3s3)2
36s10
5) (8d4)2
64d8
6) (d 3d2)3
27d9
7) (3s2 s 2 )3
216s9
8) (3c4g )4
81c16
g4
9) (3n3 4n n2)3
1728n18
10) (2b2 b2)3
8b12
11) (z 2z2 z3)3
8z18
12) (6ky5)3
216k3y
15
13) (2h2 3h3 h )2
36h12
14) (3n2 n3 4n )2
144n12
-
7/21/2019 Algebra Exponents Practice
21/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Powers of ProductsPowers of Products
Simplify the exponents.
1) (2h2 h2)3
2) (5n2y5)2
3) (4n3 n )2
4) (4d3 3d )3
5) (2y 3y3)3
6) (4z2 z 2 )3
7) (4n3b )2
8) (2b3 4b b2)2
9) (2s3 3s2 s )3
10) (4w2)4
11) (2b 4b3 b3)2
12) (4d3 d3 2d )2
13) (3cw2)3
14) (3w2 4w3)3
-
7/21/2019 Algebra Exponents Practice
22/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Powers of ProductsPowers of Products
Simplify the exponents.
1) (2h2 h2)3
8h12
2) (5n2y5)2
25n4y
10
3) (4n3 n )2
16n8
4) (4d3 3d )3
1728d12
5) (2y 3y3)3
216y12
6) (4z2 z 2 )3
512z9
7) (4n3b )2
16n6b
2
8) (2b3 4b b2)2
64b12
9) (2s3 3s2 s )3
216s18
10) (4w2)4
256w8
11) (2b 4b3 b3)2
64b14
12) (4d3 d3 2d )2
64d14
13) (3cw2)3
27c3w
6
14) (3w2 4w3)3
1728w15
-
7/21/2019 Algebra Exponents Practice
23/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Powers of Products and QuotientsPowers of Products and Quotients
Simplify the exponents.
1) (4h3 2h3 h )2
2) (2r 4r3)2
3) (3n2 n 4 )3
4) (8s5w3)5
5) (3w2 w3 2w )2
6) (3nb5)4
7) (6
3
6
__ )2
8) (3
4
33
__ )2
9) (3z
5
6z
__ )3
10) (b
b6
__ )3
11) (c
6
c3
_ )3
12) (8d
2d2
___ )3
-
7/21/2019 Algebra Exponents Practice
24/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Powers of Products and QuotientsPowers of Products and Quotients
Simplify the exponents.
1) (4h3 2h3 h )2
64h14
2) (2r 4r3)2
64r8
3) (3n2 n 4 )3
1728n9
4) (8s5w3)5
32768s25
w15
5) (3w2 w3 2w )2
36w12
6) (3nb5)4
81n4b
20
7) (6
3
6
__ )2
64
8) (3
4
33
__ )2
32
9) (3z
5
6z
__ )3
z12
8
__
10) (b
b6
__ )3
1
b15
__
11) (c
6
c3
_ )3
c9
12) (8d
2d2
___ )3
64
d3
__
-
7/21/2019 Algebra Exponents Practice
25/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Powers of Products and QuotientsPowers of Products and Quotients
Simplify the exponents.
1) (4r3 2r3 r )2
2) (2r 4r3)2
3) (4g2 2g3)2
4) (n 2n2 n2)3
5) (3z2 z3)3
6) (5n3c )5
7) (6
3
6
__ )2
8) (3
2
33
__ )3
9) (2k
4
5k
__ )2
10) (n
n5
__ )3
11) (g
2
g6
__ )3
12) (6g
8g2
___ )3
-
7/21/2019 Algebra Exponents Practice
26/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Powers of Products and QuotientsPowers of Products and Quotients
Simplify the exponents.
1) (4r3 2r3 r )2
64r14
2) (2r 4r3)2
64r8
3) (4g2 2g3)2
64g10
4) (n 2n2 n2)3
8n15
5) (3z2 z3)3
27z15
6) (5n3c )5
3125n15
c5
7) (6
3
6
__ )2
64
8) (3
2
33
__ )3
1
33
__
9) (2k
4
5k
__ )2
4k6
25
__
10) (n
n5
__ )3
1
n12
__
11) (g
2
g6
__ )3
1g
12__
12) (6g
8g2
___ )3
27
64g3
____
-
7/21/2019 Algebra Exponents Practice
27/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Powers of QuotientsPowers of Quotients
Simplify the exponents.
1) (7dr
6
9d2r
3
____ )3
2) (8g
4w
2
7g3w
5
____ )2
3) (6w
4
2w5d
3
____ )2
4) (k
k2
_ )2
5) (8
3
8
__ )3
6) (5h
4
8h
___ )2
7) (2g
6g3
___ )2
8) (9b
3
4b2
___ )3
9) (9w
3k
4
5wk6
____ )3
10) (r6
r3
_ )2
11) (6
4
66
__ )2
12) (ng
7n3g
6
____ )3
-
7/21/2019 Algebra Exponents Practice
28/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Powers of QuotientsPowers of Quotients
Simplify the exponents.
1) (7dr
6
9d2r
3
____ )3
343r9
729d3
_____
2) (8g
4w
2
7g3w
5
____ )2
64g2
49w6
____
3) (6w
4
2w5d
3
____ )2
9
w2d
6
___
4) (k
k2
_ )2
1
k2
_
5) (8
3
8
__ )3
86
6) (5h
4
8h
___ )2
25h6
64
____
7) (2g
6g3
___ )2
1
9g4
___
8) (9b
3
4b2
___ )3
729b3
64
_____
9) (9w
3k
4
5wk6
____ )3
729w6
125k6
_____
10) (r6
r3
_ )2
r6
11) (6
4
66
__ )2
16
4__
12) (ng
7n3g
6
____ )3
1
343n6g
15
_______
-
7/21/2019 Algebra Exponents Practice
29/30
Name :
Teacher : Date :
Score :
Math-Aids.Com
Powers of QuotientsPowers of Quotients
Simplify the exponents.
1) (5h
6
2h
___ )2
2) (6kh
3
9k5h
4
____ )3
3) (2g
7g2
___ )3
4) (4r6y4
2r5y
3
____ )2
5) (5w
2
9w4r
6
____ )2
6) (y
4
y2
_ )2
7) (7n
6
4n5
___ )3
8) (ky
5k3y
5
____ )3
9) (2k
3y
5
4ky2
____ )3
10) (62
63
__ )3
11) (n
n3
__ )3
12) (6
2
6
__ )3
-
7/21/2019 Algebra Exponents Practice
30/30
Name :
Teacher : Date :
Score :
Powers of QuotientsPowers of Quotients
Simplify the exponents.
1) (5h
6
2h
___ )2
25h10
4
____
2) (6kh
3
9k5h
4
____ )3
8
27k12
h3
______
3) (2g
7g2
___ )3
8
343g3
_____
4) (4r6y4
2r5y
3
____ )2
4r2y
2
5) (5w
2
9w4r
6
____ )2
2581w
4r
12______
6) (y
4
y2
_ )2
y4
7) (7n
6
4n5
___ )3
343n3
64
_____
8) (ky
5k3y
5
____ )3
1
125k6y
12
______
9) (2k
3y
5
4ky2
____ )3
k6y
9
8
___
10) (62
63
__ )3
1
63
__
11) (n
n3
__ )3
1n
6__
12) (6
2
6
__ )3
63