ALGEBRA 1

Lesson 7-4 Warm-Up

ALGEBRA 1

“More Multiplication Properties of Exponents” (7-4)

What happens when you raise a power to a power?

Rule: When you raise a power to a power [Example: (am)n ], multiply the powers together.

Example: (72)3 = (72) · (72) · (72) = (7 · 7) · (7 · 7) · (7 · 7) = 76

Example: (a6)2 = a6 · a6 = (a · a · a · a · a · a) · (a · a · a · a · a · a) = a12(am)n · amn

ALGEBRA 1

Simplify (a3)4.

Multiply exponents when raising a power to a power.(a3)4 = a3 • 4

Simplify.= a12

More Multiplication Properties of ExponentsLESSON 7-4

Additional Examples

ALGEBRA 1

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.

More Multiplication Properties of Exponents

LESSON 7-4

Additional Examples

ALGEBRA 1

“More Multiplication Properties of Exponents” (7-4)

What happens when you raise a product (for example, a variable and a coefficient, like 4x) to a power?

Rule: When you raise a product to a power [Example: (ab)m, where a and b are nonzero numbers), raise each multiplicand (a and b) to the power separately ].

Example: (3x)4 = 34 x4 = 3 · 3 · 3 · 3 · x4 = 81x4

Example:

(ab)n = an · bn

ALGEBRA 1

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.

More Multiplication Properties of ExponentsLESSON 7-4

Additional Examples

ALGEBRA 1

Simplify (4xy3)2(x3)–3.

(4xy3)2(x3)–3 = 42 • x2 • (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.

More Multiplication Properties of ExponentsLESSON 7-4

Additional Examples

16y6

x7= Simplify.

= • • Change negative exponents into positive exponents.

161

1x7

y6

1

ALGEBRA 1

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 = 10(8 • 2) .

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

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

= 9 1018 joulesSimplify.Write in scientific notation and add label.

More Multiplication Properties of ExponentsLESSON 7-4

Additional Examples

ALGEBRA 1

Simplify each expression.

1. (x4)5 2. x(x5y–2)3

3. (5a4)3 4. (1.5 105)2

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

x20x16

y6

125a122.25 1010

432w2b6

4.8 104

More Multiplication Properties of ExponentsLESSON 7-4

Lesson Quiz