Lesson 7-4 Warm-Up

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Lesson 7-4 Warm-Up
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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
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More Multiplication Properties of Exponents
LESSON 7-4
Additional Examples
Simplify (a3)4.
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More Multiplication Properties of Exponents
LESSON 7-4
Additional Examples
Simplify b2(b3)2.
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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
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More Multiplication Properties of Exponents
LESSON 7-4
Additional Examples
Simplify (4x3)2.
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More Multiplication Properties of Exponents
LESSON 7-4
Additional Examples
Simplify (4xy3)2(x3)3.
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More Multiplication Properties of Exponents
LESSON 7-4
Additional Examples
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.
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More Multiplication Properties of Exponents
LESSON 7-4
Lesson Quiz
Simplify each expression. 1. (x4)5 2. x(x5y2)3 3
. (5a4)3 4. (1.5 ? 105)2 5. (2w2)4(3w2b2)3 6. (3
? 105)(4 ? 104)2
x20
125a12
2.25 ? 1010
432w2b6
4.8 ? 104