1. Multiplication Properties of Exponents
ALGEBRA 1 LESSON 1-6
(For help, go to Lesson 1-6.)
Rewrite each expression using exponents.
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)1
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2. Multiplication Properties of Exponents
ALGEBRA 1 LESSON 1-6
Solutions
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 • 5 • 5 • s • s • s = 53 • s3 = 53s3
5. –54 = –(5 • 5 • 5 • 5) = –(25 • 25) = –625
6. (–5)4 = (–5)(–5)(–5)(–5) = (25)(25) = 625
7. (–5)1 = –5
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3. Multiplication Properties of Exponents
ALGEBRA 1 LESSON 1-6
Rewrite each expression using each base only once.
Add exponents of powers with the
same base.
73 + 2 = a.
73 • 72
= 75
Simplify the sum of the exponents.
Think of to add the exponents.
42 + 1 = b.
42 • 41
= 43
Simplify the sum of the exponents.
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4. Multiplication Properties of Exponents
ALGEBRA 1 LESSON 1-6
Simplify each expression. a.
p2 • p • p5
Add exponents of powers with the same base. p =
= p 8
Simplify.
4x6 • 5x4 b.
Commutative Property of Multiplication
(4 • 5)(x 6 • x 4) =
Add exponents of powers with the same base.
= 20(x 6+4)
Simplify.
= 20x 10
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5. Multiplication Properties of Exponents
ALGEBRA 1 LESSON 1-6
Simplify each expression. a.
a 2 • b 4 • a 5
Commutative Property of Multiplication
a 2 • a 5 • b 4 =
= a • b 4
Add exponents of powers with the same base.
Simplify.
a 7 b 4 =
Commutative and Associative Properties of Multiplication
(2 • 3 • 4)(p 3)(q • q 4) = b.
2q • 3p3 • 4q4
= 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.
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6. Multiplication Properties of Exponents
ALGEBRA 1 LESSON 1-6
Simplify each expression.
1. 34 • x5 • 3x2
3. (3  104)(5  102) 4. (7  104)(15  105) 39
12x7
15  106
105  109
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7. More Multiplication Properties of Exponents
ALGEBRA 1 LESSON 1-6
(For help, go to Lesson 1-6.)
Rewrite each expression using each base only once.
1. 32 • 32 • • 23 • 23 • 23
3. 57 • 57 • 57 • • 7 • 7
Simplify.
5. x3 • x3 6. a2 • a2 • a2
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8. More Multiplication Properties of Exponents
ALGEBRA 1 LESSON 1-6
Solutions
• 32 • 32 = 3( ) = 36
• 23 • 23 • 23 = 2( ) = 212
• 57 • 57 • 57 = 5( ) = 528
4. 7 • 7 • 7 = 73
5. x3 • x3 = x(3 + 3) = x6
6. a2 • a2 • a2 = a( ) = a6
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9. More Multiplication Properties of Exponents
ALGEBRA 1 LESSON 1-6
Simplify (a3)4.
Multiply exponents when raising a power to a power.
(a3)4 = a3 • 4
Simplify.
= a12
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10. More Multiplication Properties of Exponents
ALGEBRA 1 LESSON 1-6
Simplify b2(b3)2.
b2(b3)2 = b2 • b3 • 2 
Multiply exponents in (b3)–2.
= b2 • b6
Simplify.
= b2 + 6
Add exponents when multiplying powers of the same base.
Simplify.
= b8
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11. More Multiplication Properties of Exponents
ALGEBRA 1 LESSON 1-6
Simplify (4x3)2.
(4x3)2 = 42(x3)2
Raise each factor to the second power.
= 42x6
Multiply exponents of a power raised to a power.
= 16x6
Simplify.
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12. More Multiplication Properties of Exponents
ALGEBRA 1 LESSON 1-6
Simplify (4xy3)2(x3)3.
(4xy3)2(x3)3 = 42x2(y3)2 • (x3)3
Raise the three factors to the second power.
= 42 • x2 • y6 • x9
Multiply exponents of a power raised to a power.
= 42 • x2 • x9 • y6
Use the Commutative Property of Multiplication.
= 42 • x11 • y6
Add exponents of powers with the same base.
16 x11y6 =
Simplify.
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13. More Multiplication Properties of Exponents
ALGEBRA 1 LESSON 1-6
Simplify each expression.
1. (x4)5 2. x(x5y2)3
3. (5x4)3 4. (15  105)2
x16y6
x20
225  1010
125x12
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