Name: Date: Lesson 1.5 Zero and Negative Exponents
Simplify expressions involving numbers raised to the zero power.
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Example
a) 43 ? 40
43 ? 40 5 43
5 43
Simplify.
5 64
Evaluate.
b) 9 ? 100 1 7 ? 101 1 5 ? 102 5 9
c)  1
Raise to the zero power.
9 ? 100 1 7 ? 101 1 5 ? 102
? 1 1 7 ? 10 1 5 ? 100
5 579
73 ⋅ 74
77
73 ⋅ 74
77
Evaluate the powers.
Simplify.
73 1 4
5 77
Use the product of powers property.
5 77 Simplify.
5 7 7 2 7
Use the quotient of powers property.
5 70
Simplify.
5 1
Evaluate.
d) (z 2 4 z 0) ? z 2 5 (z 2 4
5 z 2 ? z 2
Simplify.
5 z 2 1 2
Use the product of powers property.
5 z 4
Simplify.
77
(z 2 4 z 0) ? z 2
1) ? z 2
Raise to the zero power.
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Name: Date: Complete.
1. 140 4 142
140 4 142 5
5
Simplify.
5
Evaluate.
4
Raise to the
power.
2. 5 ? 102 1 5 ? 101 1 5 ? 100
5 ? 102 1 5 ? 101 1 5 ? 100
5
?
?
5
?
1
Simplify.
Evaluate.
65 6
60
65 6
5
60
Use the
5
Simplify.
5
Use the
5
Simplify.
5
Evaluate.
4.
of powers property.
of powers property.
a3 a2 a0
4
a
a3 a2 a0
5
4
a
Use the
5
Simplify.
5
Use the
5
Simplify.
5
Evaluate.
of powers property.
of powers property.
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3.
1
Evaluate the powers.
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Name: Date: Simplify each expression and evaluate where applicable.
5. 32 ? 30 ? 32
2 2
   
3 3
6.1.2 ? 103 2 2 ? 102 2 1 ? 103
2
7.
6
0
f 8 f 2
8. f 0 f 4
4 5
   
5  8 
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2
9. (w 4 4 w 0) ? (y 5 4 y 4)
10.
7
 
 9
2
0
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Name: Date: Write using a positive exponent.
Example
a) 925 ? 914
Method 1
1
 914
95
914
5 95 925 ? 914 5
5 914 2 5
5 99
Write using a positive exponent.
Simplify.
Use the quotient of powers property.
Simplify.
Method 2
b) 925 ? 914 5 925 1 14
5 99
Use the power of products property.
Simplify.
h3
5
h
1
1
 h3 h5
1
5 3 5
h  h
1
5 315
h
1
5 8
h
h3
5
h
5
Write using a positive exponent.
Simplify.
Use the product of powers property.
Simplify.
c) 12g2 4 4g26 5
Write the division as a fraction.
Rewrite the fraction as the product of two fractions.
5 3  g22(26)
Use the quotient of powers property.
5 3g8
Simplify.
12g2 4 4g26
12g2 4g26
12 g2
5  26 4 g
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38 Chapter 1 Lesson 1.5
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Name: Date: Complete.
11. 224 4 222
224 4 222 5
Use the
5
Simplify.
5
Write using a
5
Evaluate.
12.
55
8
5
55
8 5
5
Use the
5
Simplify.
5
Write using a
5
Evaluate.
of powers property.
exponent.
of powers property.
exponent.
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13. k23 4 10k28
k23 4 10k28 5
5
?
Rewrite the fraction as the
5
?
Use the
5
Write the
as a fraction.
of two fractions.
of powers property.
Simplify.
14. 20y29 4 (2y2 ? 5y23)
20y29 4 (2y2 ? 5y23) 5
5
?
Rewrite the fraction as the
5
?
Use the
5
?
Use the
5
Simplify.
5
Write using a
Write the expression as a
.
of two fractions.
of powers property to the numerator.
of powers property to the resulting
new fraction.
exponent.
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Name: Date: Simplify each expression. Write your answer using a positive exponent.
16.
17. 3d27 4 6d24
18.9x25 ? (36x6 4 4x2)
g2
19. 2g12 ? g 6 20.125y4 4 5y28
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r
r 2
15. 1002 ? 1003 ? 10025
40 Chapter 1 Lesson 1.5
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