Exponent Rules Review Worksheet - Hazleton Area High School
[Pages:2]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.
xm xn xmn
Example 1: x x3 x4 x134 x8 Example 2: 2x2 y 3x3 y4 23 x2 x3 y y4 6x5 y5
Power Rule: When raising monomials to powers, multiply the exponents.
xm n xmn
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 xmn xn
Example 5:
x3 x2
x3(2) x5
Example 6: 56 562 54 52
Example 7:
36m3n5 9mn4
36 m3 9 m
n5 n4
4m2n
Simplify each of the following. Copy the problem. Work on your own paper.
1) a a2 a3
2) (2a2b)(4ab2) 3) (6x2)(-3x5)
4) b3 b4 b7 b
5) (3x3)(3x4)(-3x2)
6) (2x2y3)2
7) (5x2y4)3
8) (6x4y6)3
9) (4x3y3)3
10) (7xy)2
11) x3 x
18c3 12)
3c2
13) 9a3b5 3ab2
14) 48c2d 4 8cd
22 y6 z8 15) 2 yz7
16) x2 x7 21) 8x0 26) 2x3
8x4
17) x2 7
22) 34 xy7
27) x3 y4
18) 2x4 5
19) 2x3 7x3
20) 70
23) 34
24) 6x0 y8 2y2 4 25) x 2y x 2y
28) 6x5 3x5 x0
29) 3st12 3
3m2n7 5
30)
m
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.
xm xn xmn
Example 1: x x3 x4 x134 x8 Example 2: 2x2 y 3x3 y4 23 x2 x3 y y4 6x5 y5
Power Rule: When raising monomials to powers, multiply the exponents.
xm n xmn
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 xmn xn
Example 5:
x3 x2
x3(2) x5
Example 6: 56 562 54 52
Example 7:
36m3n5 9mn4
36 m3 9 m
n5 n4
4m2n
Simplify each of the following. Copy the problem. Work on your own paper.
1) a a2 a3
2) (2a2b)(4ab2) 3) (6x2)(-3x5)
4) b3 b4 b7 b
5) (3x3)(3x4)(-3x2)
6) (2x2y3)2
7) (5x2y4)3
8) (6x4y6)3
9) (4x3y3)3
10) (7xy)2
11) x3 x
18c3 12)
3c2
13) 9a3b5 3ab2
14) 48c2d 4 8cd
22 y6 z8 15) 2 yz7
16) x2 x7 21) 8x0 26) 2x3
8x4
17) x2 7
22) 34 xy7
27) x3 y4
18) 2x4 5
19) 2x3 7x3
20) 70
23) 34
24) 6x0 y8 2y2 4 25) x 2y x 2y
28) 6x5 3x5 x0
29) 3st12 3
3m2n7 5
30)
m
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