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

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

8-4

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

8-4

You TryYou Try

1. (c2)6(c6)4 **Remember to follow order of operations c12 • c24

c36

2. (d3)2d4

d6 • d4

d10

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

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

8-4

You TryYou Try

(4g5) -2

4-2(g5) -2

4-2g-10

1 16g10

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

8-4

You Try:You Try:

(2a3)5(3ab2)3

25(a3)5 •33a3(b2)3

25a15 • 33a3b6

32a15 • 27a3b6

864a18b6