1. Multiplication Properties of Exponents
ALGEBRA 1 LESSON 8-3
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 – 2 as (–2) to add the exponents.
– 2 = b.
44 • 41 • 4–2
= 43
Simplify the sum of the exponents.
Add exponents of powers with the
same base.
68 + (–8) = c.
68 • 6–8
= 60
Simplify the sum of the exponents.
Use the definition of zero as an exponent.
= 1
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2. You try:
53 · 56 59
24 · 2 -3 21

3. Multiplication Properties of Exponents
ALGEBRA 1 LESSON 8-3
Simplify each expression. a.
p2 • p • p5
Add exponents of powers with the same base. p =
= p 8
Simplify.
4x6 • 5x–4 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 2
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4. You try:
n2 · n3 · 7n
7n6

5. Multiplication Properties of Exponents
ALGEBRA 1 LESSON 8-3
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. You try:
2y3 · 7x2 · 2y4
28 · x2 · y7

7. 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) =
Commutative and Associative Properties of Multiplication
(3 • 7)(10–3 • 10–5)
= 21  10–8
Simplify.
= 2.1  101 • 10–8
Write 21 in scientific notation.
= 2.1  (– 8)
Add exponents of powers with the same base.
= 2.1  10–7
Simplify.
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8. You try:
(1.5 · 10-2) ( 3 · 104)
4.5 · 102

9. Multiplication Properties of Exponents
ALGEBRA 1 LESSON 8-3
pages 407–410  Exercises
1. 210 2.
3. 1
4. (0.99)3
5. 69
6. 1
7. c5
8. 3r 5
9. 10t –7
10. 56x 6
11. 3x4
22. 6  105
23. 6  109
24. 4  103
 10–5
 10–7
1.5  1022
2.55 x 1013
1.08 x 1021
3.84 x 105 9 -4 -3
12. –4.8n3
13. b3
14. –7
15. –45a4
16.
17. 45x 7y 6
18. 12a6c8
19. x10y2
20. a8b
21. – 25 58 y3 x
240m3 r
8-3

10. Multiplication Properties of Exponents
ALGEBRA 1 LESSON 8-3
Simplify each expression.
1. 34 • x5 • 3x–2
3. (3  104)(5  102) 4. (7  10–4)(1.5  105)
5. (–2w –2)(–3w2b–2)(–5b–3)
6. What is 2 trillion times 3 billion written in scientific notation? 39
12x3
1.5  107
1.05  102 30 b5 –
6  1021
8-3