Download presentation

Presentation is loading. Please wait.

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

Similar presentations

© 2024 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google