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Multiplication Properties of
Exponents
Rewrite each expression
using exponents.
ALGEBRA 1 LESSON 8-3
(For help, go to Lesson 1-6.)
1.
t•t•t•t•t•t•t
2. (6 – m)(6 – m)(6 – m)
3.
(r + 5)(r + 5)(r + 5)(r + 5)(r + 5)
4. 5 • 5 • 5 • s • s • s
Simplify.
5. –54
6.
(–5)4
7. (–5)0
8.
(–5)–4
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Multiplication Properties of
Exponents
Solutions
ALGEBRA 1 LESSON 8-3
1. t • t • t • t • t • t • t = t7
2. (6 – m)(6 – m)(6 – m) = (6 – m)3
3. (r + 5)(r + 5)(r + 5)(r + 5)(r + 5) = (r + 5)5
4.
5.
6.
7.
8.
5 • 5 • 5 • s • s • s = 53 • s3 = 53s3
–54 = –(5 • 5 • 5 • 5) = –(25 • 25) = –625
(–5)4 = (–5)(–5)(–5)(–5) = (25)(25) = 625
(–5)0 = 1
(–5)–4 = (– 1 )4
5
= (– 1 )(– 1 )(– 1 )(– 1 )
5
5
= ( 1 )( 1 )
25 25
= 1
625
5
5
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Multiplication Properties of
Exponents
Rewrite each expression using each base only once.
ALGEBRA 1 LESSON 8-3
a. 73 • 72 = 73 + 2
= 75
b. 44 • 41 • 4–2 = 44 + 1 – 2
= 43
Add exponents of powers with the
same base.
Simplify the sum of the exponents.
Think of 4 + 1 – 2 as 4 + 1 + (–2) to
add the exponents.
Simplify the sum of the exponents.
= 60
Add exponents of powers with the
same base.
Simplify the sum of the exponents.
=1
Use the definition of zero as an exponent.
c. 68 • 6–8 = 68 + (–8)
4-3
Multiplication Properties of
Exponents
Simplify each expression.
ALGEBRA 1 LESSON 8-3
a.
p2 • p • p5 = p 2 + 1 + 5
= p8
Add exponents of powers with the same base.
Simplify.
b. 4x6 • 5x–4 = (4 • 5)(x 6 • x –4) Commutative Property of Multiplication
= 20(x 6+(–4))
Add exponents of powers with the
same base.
= 20x 2
Simplify.
4-3
Multiplication Properties of
Exponents
Simplify each expression.
ALGEBRA 1 LESSON 8-3
a.
a 2 • b –4 • a 5 = a 2 • a 5 • b –4
Commutative Property of Multiplication
Add exponents of powers with the
same base.
= a 2 + 5 • b –4
a7
= 4
b
Simplify.
b. 2q • 3p3 • 4q4 = (2 • 3 • 4)(p 3)(q • q 4)
Commutative and Associative
Properties of Multiplication
= 24(p 3)(q 1 • q 4)
Multiply the coefficients. Write q as q 1.
= 24(p 3)(q 1 + 4)
Add exponents of powers with the
same base.
= 24p 3q 5
Simplify.
4-3
Multiplication Properties of
Exponents
ALGEBRA 1 LESSON 8-3
Simplify (3  10–3)(7  10–5). Write the answer in scientific
notation.
(3 
10–3)(7

10–5) =
(3 • 7)(10–3 • 10–5)
Commutative and Associative
Properties of Multiplication
= 21  10–8
Simplify.
= 2.1  101 • 10–8
Write 21 in scientific notation.
= 2.1 
Add exponents of powers with the
same base.
101 + (– 8)
= 2.1  10–7
Simplify.
4-3
Multiplication Properties of
Exponents
ALGEBRA 1 LESSON 8-3
The speed of light is 3  108 m/s. If there are1  10–3 km in
1 m, and 3.6  103 s in 1 h, find the speed of light in km/h.
Speed of light =
meters
kilometers
seconds
•
•
seconds
meters
hour
m
km
s
= (3  108) s • (1  10–3)
• (3.6  103)
m
h
= (3 • 1 • 3.6)  (108 • 10–3 • 103)
= 10.8  (108 + (– 3) + 3)
Use dimensional analysis.
Substitute.
Commutative and Associative
Properties of Multiplication
Simplify.
4-3
Multiplication Properties of
Exponents
ALGEBRA 1 LESSON 8-3
(continued)
= 10.8  108
Add exponents.
= 1.08  101 • 108
Write 10.8 in scientific notation.
= 1.08  109
Add the exponents.
The speed of light is about 1.08  109 km/h.
4-3
Multiplication Properties of
Exponents
Simplify each expression.
ALGEBRA 1 LESSON 8-3
1. 34 • 35
2. 4x5 • 3x–2
39
3. (3  104)(5  102) 1.5  107
12x3
4. (7  10–4)(1.5  105) 1.05  102
5. (–2w –2)(–3w2b–2)(–5b–3) – 305
b
6. What is 2 trillion times 3 billion written in scientific notation? 6  1021
4-3