Algebra Exponents Practice

7/21/2019 Algebra Exponents Practice

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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


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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


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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

____


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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

___


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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

_____


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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

___


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Exponents with Multiplication and DivisionExponents with Multiplication and Division


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

__


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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


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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


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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

___


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Exponents and MultiplicationExponents and Multiplication


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


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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


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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


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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


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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


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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

_____


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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


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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


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Powers of ProductsPowers of Products


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


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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


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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


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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


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Powers of Products and QuotientsPowers of Products and Quotients


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


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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

__


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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


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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

____


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Powers of QuotientsPowers of Quotients


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


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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

_______


29/30

Name :

Teacher : Date :

Score :

Math-Aids.Com



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


30/30

Name :

Teacher : Date :

Score :



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

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