1. Lesson 7-4 Warm-Up

2. “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

3. Multiply exponents when raising a power to a power. (a3)4 = a3 • 4
More Multiplication Properties of Exponents
LESSON 7-4
Additional Examples
Simplify (a3)4.
Multiply exponents when raising a power to a power.
(a3)4 = a3 • 4
Simplify.
= a12

4. Multiply exponents in (b3)–2.
More Multiplication Properties of Exponents
LESSON 7-4
Additional Examples
Simplify b2(b3)–2.
b2(b3)–2 = b2 • b3 • (–2) 
Multiply exponents in (b3)–2.
= b2 • b–6
Simplify.
= b2 + (–6)
Add exponents when multiplying powers of the same base.
Simplify.
= b–4 1 b4 =
Write using only positive exponents.

5. “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

6. Raise each factor to the second power.
More Multiplication Properties of Exponents
LESSON 7-4
Additional Examples
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.

7. (4xy3)2(x3)–3 = 42 • x2 • (y3)2 • (x3)–3
More Multiplication Properties of Exponents
LESSON 7-4
Additional Examples
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. 16 1
= • •
Change negative exponents into positive exponents. 1 x7 y6 1
16y6 x7 =
Simplify.

8. Raise each factor within parentheses to the second power.
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.
102 • (3  108)2 = 102 • 32 • (108)2
Raise 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 •
Add exponents of powers with the same base.
= 9  joules
Simplify.
Write in scientific notation and add label.

9. Simplify each expression. 1. (x4)5 2. x(x5y–2)3
More Multiplication Properties of Exponents
LESSON 7-4
Lesson Quiz
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
x16 y6
x20
125a12
2.25  1010
432 w2b6
4.8  104