ALGEBRA 1 LESSON 8-4ALGEBRA 1 LESSON 8-4

(For help, go to Lesson 8-3.)

Rewrite each expression using each base only once.

1. 32 • 32 • 32 2. 23 • 23 • 23 • 23

3. 57 • 57 • 57 • 57 4. 7 • 7 • 7

Simplify.

5. x3 • x3 6. a2 • a2 • a2

7. y–2 • y–2 • y–2 8. n–3 • n–3

More Multiplication Properties of Exponents

4-4

ALGEBRA 1 LESSON 8-4ALGEBRA 1 LESSON 8-4

1. 32 • 32 • 32 = 3(2 + 2 + 2) = 36

2. 23 • 23 • 23 • 23 = 2(3 + 3 + 3 + 3) = 212

3. 57 • 57 • 57 • 57 = 5(7 + 7 + 7 + 7) = 528

4. 7 • 7 • 7 = 73

5. x3 • x3 = x(3 + 3) = x6

6. a2 • a2 • a2 = a(2 + 2 + 2) = a6

7. y–2 • y–2 • y–2 = y(–2 + (–2) + (–2)) = y–6 =

8. n–3 • n–3 = n(–3 + (–3)) = n–6 =

1 y 6

1 n 6

More Multiplication Properties of ExponentsSolutions

4-4

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 8-4More Multiplication Properties of Exponents

4-4

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 8-4More Multiplication Properties of Exponents

4-4

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 8-4More Multiplication Properties of Exponents

4-4

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 8-4More Multiplication Properties of Exponents

4-4

An object has a mass of 102 kg. The expression

102 • (3 108)2 describes the amount of resting energy in joules the

object contains. Simplify the expression.

102 • (3 108)2 = 102 • 32 • (108)2Raise each factor within parentheses to the second power.

= 102 • 32 • 1016 Simplify (108)2.

= 32 • 102 • 1016 Use the Commutative Property of Multiplication.

= 32 • 102 + 16 Add exponents of powers with the same base.

= 9 1018Simplify.Write in scientific notation.

ALGEBRA 1 LESSON 8-4ALGEBRA 1 LESSON 8-4More Multiplication Properties of Exponents

4-4

ALGEBRA 1 LESSON 8-4ALGEBRA 1 LESSON 8-4

Simplify each expression.

1. (x4)5 2. x(x5y–2)3

3. (5x4)3 4. (1.5 105)2

5. (2w–2)4(3w2b–2)3 6. (3 10–5)(4 104)2

x20 x16

y6

125x12 2.25 1010

432b6w2 4.8 103

More Multiplication Properties of Exponents

4-4