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Lesson 8.4 Multiplication Properties of ExponentsLesson 8.4 Multiplication Properties of Exponents
Property: Raising a Power to a PowerFor every nonzero number a and integers m and n, (am)n = amn
Examples: (54)2 = 54•2
58
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Simplify (a3)4.
Multiply exponents when raising a power to a power.
(a3)4 = a3 • 4
Simplify.= a12
ALGEBRA 1 LESSON 8-4ALGEBRA 1 LESSON 8-4
Simplifying a Power Raised to a PowerSimplifying a Power Raised to a Power
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Simplify b2(b3)–2.
b2(b3)–2 = b2 • b3 • (–2) Multiply exponents in (b3)–2.
= b2 + (–6) Add exponents when multiplying powers of the same base.
Simplify. = b–4
= b2 • b–6 Simplify.
1 b4= Write using only positive exponents.
ALGEBRA 1 LESSON 8-4ALGEBRA 1 LESSON 8-4
Simplifying an Expression With PowersSimplifying an Expression With Powers
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You TryYou Try
1. (c2)6(c6)4 **Remember to follow order of operations c12 • c24
c36
2. (d3)2d4
d6 • d4
d10
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Raising a Product to a PowerRaising a Product to a Power
Property: Raising a Product to a Power
For every nonzero number a and b and integer n,
(ab)n = anbn.
Example: (3x)4 = 34 x4
81x4
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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.
ALGEBRA 1 LESSON 8-4ALGEBRA 1 LESSON 8-4
Simplifying a Product Raised to a PowerSimplifying a Product Raised to a Power
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You TryYou Try
(4g5) -2
4-2(g5) -2
4-2g-10
1 16g10
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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 • x–9 Multiply exponents of a power raised to a power.
= 42 • x2 • x–9 • y6 Use the Commutative Property of Multiplication.
= 42 • x–7 • y6 Add exponents of powers with the same base.
16y6
x7= Simplify.
ALGEBRA 1 LESSON 8-4ALGEBRA 1 LESSON 8-4
Simplifying a Product Raised to a PowerSimplifying a Product Raised to a Power
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You Try:You Try:
(2a3)5(3ab2)3
25(a3)5 •33a3(b2)3
25a15 • 33a3b6
32a15 • 27a3b6
864a18b6