Name: _________________
Exponent Rules
RULE: When you __________ powers with the same base, you ________ the exponents
Example:
1) a7∙a4 = a11
2) 83 ∙89 = 812
3) w5 ∙w7 ∙ w-3 = w9
4) x8 ∙y7∙y10∙x-10= x-2y17
5) 3x10∙5x4 = 15x14
6) (-8j4)(-2j7) = 16j11
Hint: Multiply coefficients, and add the exponents
Try These:
1) x4 ∙ x8 =
2) 107 ∙ 105 =
3) 12x5(4x3) =
4) x7 ∙ x -8 ∙ x4 =
5) s4 ∙ t2 ∙ s-1 ∙ t9 =
6) (-3x4)(7x3)=
________________________________________________________________________
RULE: When you ____________ powers with the same base, you ________ the exponents
(Top minus bottom)
Example:
1) y10 = y6
2) 98 = 96
3) d4 = d-5
y4
92
d9
4) x5y4 = x-2y3
x7y
Hint: Any variable with out a power has an understood exponent of 1
Example:
y means y1
5) 28a4b-3c10 = 4a7b-8c7
7 a-3b5c3
Hint: Divide the coefficients, and subtract the exponents
Example: a4 = a7, because 4 – (-3) = 7
a-3
Try These:
1) x12 =
x9
2) 88 =
83
3) p2 =
p7
4) 16x7 =
2x2
5) a9b6c2 =
a4b c7
6) 28x15y7 =
7x20y3
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1) a2 ∙ a3 =
2) b4 ∙ b6 =
3) x5 ∙ x =
4) 52 ∙ 54 =
5) m3 ∙ n4 ∙ m5
6) x2 ∙ y3 ∙ y2 ∙ x =
7) p3 ∙q5 ∙ p7 =
8) s4 ∙ t5 ∙ t3 =
9) (3m3)(2m5) =
10) (-5m2)(-2m4) =
11) 43 ∙ 44 =
12) (6p5)(8p4) =
13) (2x2y)(3xy4) =
14) (-2a2b3)(3a4) =
15) (5x2y3)(-2x4y5)=
16) (3m2n5)(-8mn2)
17) 25 =
23
18) 54 =
57
19) a10 =
a7
20) x12 =
x8
21) m5n2 =
m8n7
22) xy6 =
x4y3
23) a3b4 =
ab2
24) 3-2 =
32
25) 6-3 =
6-5
26) d-3 =
d-9
27) a-6 =
a4
28) x10 =
x-7
29) a4b-7c =
a8b3c-6
30) s-14 =
s-10
31) a2b-3 =
a-4b3
32) p-4q-6 =
pq-1
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RULE: To raise a power to a ___________, _____________ the exponents
Example:
1) (x5)7 = x35
2) (x3)-2 = x-6
3) (4x5)2 =
Hint: Square each part of 4x5
4) (3a5b)3 =
Hint: Raise each part of (3a5b) to the third power
Try These:
1) (x6)2 =
2) (y4)7 =
5) x5 ∙ (x7)3 =
3) (ab2)6 =
5) (6x3y4)2 =
4) c3 ∙ (c4)9 =
6) (3a7b5)4 =
________________________________________________________________________
RULE: Any number raised to the power of __________, equals ___________
Example:
1) 170 = 1
2) (-3)0 = 1
3) -50 = -1
4) (8x4y7)0 = 1
Hint: Whole expression is raised to 0 power
5) 2x0 = 2∙1 = 2
Hint: Only x is raised to the power of 0
Try These:
1) 20070 =
2) x0 =
3) (6x2y-3)0 =
4) -70 =
5) (-2)0 =
6) 7x0 =
________________________________________________________________________
RULE: a-n is the reciprocal of 1/an (Cross the Border)
Example
1) x-5 = 1
2) 1 = a8
3) x3y-4 = x3z10
x5
4) 2x-6 = 2
x6
Try These:
1) a-8 =
4) 5x2y-4 =
a-8
5) y-4 ∙ (y3)-2 = y-4 ∙ y-6 = y-10 = 1
y10
z-10
y4
6) (x5y-3)-2 = (x5)-2 ∙ (y-3)-2 = x-10y6= y6
x10
2) 1 =
7-20
3) a11b-6 =
c-4d5
5) a10∙ (a6)-3 =
6) (g3h)-3 =
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Power to a Power Practice:
1) (x8)4 =
2) (y4)7 =
3) (a4b)3 =
4) (c5)3 • c2=
5) (3x2y6)3 =
6) (4ab3)2 =
7) (4x6y7)0=
8) 15,7890 =
9) 4x0 =
10) (-5)0 =
11) -20 =
12) r0 =
13)160 =
14) 4-2 =
15) 3-3 =
16) x -7 =
17) (4x3y6)0 =
18) m7n-6 =
19) -50 =
20) (-6)0 =
21) 5a-2b-4c9 =
22) 1 =
a-2
23) a-2b6 =
c-4d7
24) 4x =
y-2
Power of Zero Practice:
Negative Exponents and more:
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Exponents Practice
`
Name: __________________
Date: _________ Period: ___
Short Answer:
1) When multiplying powers with the same base, you must ________________________
2) When dividing powers with the same base, you must ___________________________
3) To raise a power to a power, you must ______________________________________
4) Any number raised to the power of zero equals _______________________________
5) How do you make a negative exponent positive? _____________________________
Simplify each expression:
6) -20
7) (-5)0
8) (82c)0
9) 24y0
Simplify each expression so that all exponents are positive:
10) 6-2
11) 3x9y-3
12) (-5)3
13) w9 x-8
y-2z -7
14) 4242
15)a6a8
16) x4y16x3
17) (-5x4)(10x3)
18) h-7h9
19) s-9s10s-12
20)
21) p19
p
1
c c
-9 -3
22) x8
x5
23) a-2b6
a9 b-3
24) (n2)7
26) (y -8)-2
27) (5x-6)3
28) w6 (w7)3
25) (4x9)2
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Exponents Practice Quiz
Algebra I
Name: __________________
Date: _________ Period: ___
Short Answer:
1) When multiplying powers with the same base, you must ________________________
2) When dividing powers with the same base, you must ___________________________
3) To raise a power to a power, you must ______________________________________
4) Any number raised to the power of zero equals _______________________________
5) How do you make a negative exponent positive? _____________________________
Simplify each expression:
6) 70
7) -50
8) (-5)0
9) 2x0
Simplify each expression so that all exponents are positive:
10) 4-3
11) 5a-2b9
12) (-4)3
13) w -2x4
y10z -9
14) 5252
15)a3a8
16)x5y10x2
17) (4x9)(10x3)
18) h-5h9
19) s-9s10s-3
20)
21) p10
p
1
c c
-4 -3
22) x5
x3
23) a6b-10
a-4 b5
24) (n4)5
25) (2x2)3
26) (y-3)7
27) (3x-6)2
28) w-5 (w2)4
29) (3x4)2 (2xy6)3
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Match each expression on the left with an equivalent expression on the right:
_______ 1) 2(x5)3
 x5 
_______ 2)  
 2
a. 8x15
3
b. x30
_______ 3) (2x5)3
c. 2x8
x15
8
8 x3
e.
125
d.
_______ 4)
2x 5
x3
f.
 2x 
_______ 5)  
 5 
6 x3
9
3
g. 4x2
h. 2x15
_______ 6) 2x5 ∙ x3
i. 2x2
_______ 7) x5 (2x)3
j. x10
k. 8x8
_______ 8) x ∙ x ∙ x
2
3
5
l. 6x8
Simplify:
9) (x3y2)(x5y4)
5 6
10) 2x3y5z7
8xy8z2
2 7
-2
12) (3xy z )(9x y z)
 7a 
13)  2 
b 
3
11) 82 ∙ 84
83
 7x 2 
14)  2 5 
x y 
0
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Scientific Notation:
Scientific Notation is in the form:
c x 10n
To write a number in scientific notation:
1) Move the decimal to the right of the first integer
2) - If the original number is greater than one, then multiply by 10n
- If the original number is less than one, then multiply it by 10-n
- N represents the number of places the decimal was moved
Examples:
1) 8,260,000 = 8.26 x 106
2) 0.00056 = 5.6 x 10-4
3) 809.26 = 8.0926 x 102
Try These:
1) 0.0000712 =
2) 26,000,000 =
3) 7015.42 =
________________________________________________________________________
To write a number in standard notation:
1) If n is positive, move the decimal n spaces to the right
2) If n is negative, move the decimal n space to the left
Examples:
1) 6 x 105 = 600000
2) 5.26 x 103 = 5260
3) 3.07 x 10-4 = 0.000307
Try These:
4) 8 x 10-6 =
5) 7.81 x 106 =
6) 1.48 x 10-5 =
________________________________________________________________________
Multiplication: Multiply the regular numbers and add the exponents
Example:
1) (3 x 108)(8 x 103) = 24 x 1011
2) (1.6 x 10-3)(4 x 108) = 6.4 x 105
Hint: 10 is a base, so it doesn’t change
Try These:
1) (4 x 1012)(2.1 x 106)
2) (7.6 x 1015) (1.2 x 10-4)
________________________________________________________________________
Division: Divide the regular numbers and subtract the exponents
1) 8 x 109 = 4 x 103
2) 9.6 x 10-2 = 3.2 x 10-5
6
2 x 10
3 x 103
Try These:
1) 12 x 108 =
4 x 105
2) 3.7 x 109 =
2.6 x 1020
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Scientific Notation Practice
Name: _______________
Period: ___ Date: ______
Write the following numbers in scientific notation:
1) 67,000,000
2) 60,100,000,000
3) 0.000204
4) 5020
5) 0.00009
8) 0.0104
6) 0.000013
7) 50,000
Write the following numbers in standard notation:
9) 5 x 10-3
10) 1.2 x 106
11) 9.0475 x 10-5
12) 12 x 103
13) 8 x 104
16) 83.2 x 10-4
14) 1.01 x 107
15) 3.0154 x 102
Simplify: Round each to the hundredths place
17) (1.8 x 106) (5.2 x 103)
18) (3.4 x 105) (2.9 x 10-8)
19) 9.02 x 1012
3.21 x 105
20) 7.2 x 10-3
4.8 x 107
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