Exponent Rules Review Worksheet
NOTE: Anything to the zero power equals 1!
Product Rule: When multiplying monomials that have the same base, add the exponents.
x m  x n  x m n
Example 1: x  x3  x4  x134  x8
Example 2:
 2x y  3x y   2   3  x
2
3
4
2
 x3  y  y 4  6 x5 y 5
Power Rule: When raising monomials to powers, multiply the exponents.
x 
m
n
 x m n
Example 3: (x2y3)4 = x2  4 y3  4 = x8y12
Example 4: (2x3yz2)3 = 23 x3  3 y3 z2  3 = 8x9y3z6
Quotient Rule: When dividing monomials that have the same base, subtract the exponents.
xm
 x mn
n
x
x3
36m3n5 36 m3 n5
56
Example 5: 2  x3( 2)  x5
Example 6: 2  562  54
Example 7:

  4  4m2 n
4
x
9mn
9 m n
5
Simplify each of the following. Copy the problem. Work on your own paper.
1) a  a2  a3
2)
6) (2x2y3)2
7) (5x2y4)3
11)
x3
x
12)
(2a2b)(4ab2)
18c3
3c 2
3)
(6x2)(-3x5)
8) (6x4y6)3
13)
9a3b5
3ab2
16) x2  x7
17)  x 2 
21) 8x0
22) 34
23)  3
2 x3
26)
8 x 4
xy 7
27) 3 4
x y
28) 6x  3x  x
7
18)  2x 4 
5
4) b3  b4  b7  b
5) (3x3)(3x4)(-3x2)
9) (4x3y3)3
10) (7xy)2
14)
5
48c 2 d 4
8cd
19) 2x3  7 x3
24) 6 x 0 y 8   2 y 2 
4
5
15)
0
29)  3st
12

3
22 y 6 z 8
2 yz 7
20) 70
4
25)  x  2 y  x  2 y 
 3m 2 n 7 
30) 

 m 
5
Exponent Rules Review Worksheet
NOTE: Anything to the zero power equals 1!
Product Rule: When multiplying monomials that have the same base, add the exponents.
x m  x n  x m n
Example 1: x  x3  x4  x134  x8
Example 2:
 2x y  3x y   2   3  x
2
3
4
2
 x3  y  y 4  6 x5 y 5
Power Rule: When raising monomials to powers, multiply the exponents.
x 
m
n
 x m n
Example 3: (x2y3)4 = x2  4 y3  4 = x8y12
Example 4: (2x3yz2)3 = 23 x3  3 y3 z2  3 = 8x9y3z6
Quotient Rule: When dividing monomials that have the same base, subtract the exponents.
xm
 x mn
n
x
x3
36m3n5 36 m3 n5
56
Example 5: 2  x3( 2)  x5
Example 6: 2  562  54
Example 7:

  4  4m2 n
4
x
9mn
9 m n
5
Simplify each of the following. Copy the problem. Work on your own paper.
1) a  a2  a3
2)
6) (2x2y3)2
7) (5x2y4)3
11)
x3
x
12)
(2a2b)(4ab2)
18c3
3c 2
3)
(6x2)(-3x5)
8) (6x4y6)3
13)
9a3b5
3ab2
16) x2  x7
17)  x 2 
21) 8x0
22) 34
23)  3
2 x3
26)
8 x 4
xy 7
27) 3 4
x y
28) 6x  3x  x
7
18)  2x 4 
5
4) b3  b4  b7  b
5) (3x3)(3x4)(-3x2)
9) (4x3y3)3
10) (7xy)2
14)
5
48c 2 d 4
8cd
19) 2x3  7 x3
24) 6 x 0 y 8   2 y 2 
4
5
15)
0
29)  3st
12

3
22 y 6 z 8
2 yz 7
20) 70
4
25)  x  2 y  x  2 y 
 3m 2 n 7 
30) 

 m 
5