Download presentation

1
**6.1 Properties of Exponents**

2/4/2013

2
**Power, Base and Exponent:**

73 Exponent: is the number that tells you how many times the base is multiplied to itself. In this example 73 means 7•7•7

3
**In general: am•an = am+n**

Product of Powers: Ex. 32 • 35 = 3•3•3•3•3•3•3 = 37 = 32+5 In general: am•an = am+n

4
**In general: (am)n = am•n**

Power of a Power: Ex. (23 )2 = (23 )• (23 ) =(2•2•2)•(2•2•2) = 26 = 23•2 In general: (am)n = am•n

5
**In general: (a •b)m =a m•b m**

Power of a Product: Ex. (4•3 )3 = (4•3 )• (4•3 ) • (4•3 ) =(4•4•4)•(3•3•3) = 4 3 •3 3 In general: (a •b)m =a m•b m

6
**In general: a0 = 1 Zero Exponent 50 = 1 40 = 1 30 = 1 ÷5 ÷5 ÷5 ÷4 ÷4**

÷3 ÷3 ÷3 In general: a0 = 1 Any base raised to a 0 power equals 1.

7
**Exponential Form Fraction Form**

32 9 31 3 30 1 = =

8
**Ex. 5-2 Ex. In general: Negative Exponent**

Negative exponent MOVES power. If the power with a negative exponent is in the numerator, the power moves to the denominator and exponent becomes positive. If the power with a negative exponent is in the denominator, the power moves to the numerator and exponent becomes positive.

9
Quotient of Powers Ex. In general:

10
Power of a Quotient Ex. In general:

11
**Example 1 ( ) 8 2 – )4 = ( ) 8 4 2 – + = ( ) 4 2 – 1 ( )4 2 – = = 16 1**

Evaluate Expressions with Negative Exponents ( ) 8 2 – )4 Product of powers property = ( ) 2 – + = ( ) 4 2 – Simplify exponent. 1 ( )4 2 – = Negative exponent property = 16 1 Evaluate power.

12
**Example 2 33 35 2 Evaluate . 33 35 2 = ( )2 32 = 34 = 81**

Evaluate Quotients with Exponents 33 35 2 Evaluate Quotient of powers property 33 35 2 = ( )2 32 = 34 Power of a power property = 81 Evaluate power. 12

13
**Evaluate the expression.**

Checkpoint Evaluate Numerical Expressions Evaluate the expression. 1. ( )3 22 ANSWER 64 ( )3 50 2. ANSWER 1 ANSWER 27 1 – 3. ( ) 5 3 – )2 4. 3 2 ANSWER 27 8

14
**Example 3 a. y x – 3 2 x 2 ( )2 y – 3 = = x 2 y – 3 2 • = x 2 y – 6 =**

Simplify Algebraic Expressions a. y x – 3 2 Power of a quotient property x 2 ( )2 y – 3 = = x 2 y – 3 2 • Power of a power property = x 2 y – 6 Simplify exponent. = x 2y 6 Negative exponent property

15
**Example 3 ( )2 5y – 3 y 5y b. = ( )2 y – 3 y 5y 52 = 25y y 5y – 3 2 •**

Simplify Algebraic Expressions ( )2 5y – 3 y 5y b. = ( )2 y – 3 y 5y 52 Power of a product property = 25y y 5y – 3 2 • Power of a power property = 25y y 5y – 6 Simplify exponent. = 25y – + Product of powers property = 25y 0 Simplify exponent. = 25 Zero exponent property 15

16
**Example 3 c. x 5y 2 – x 3y 6 = x – 3 5 y 6 ( 2) = x 2y 8 – = y 8 x 2**

Simplify Algebraic Expressions c. x 5y 2 – x 3y 6 = x – y 6 ( 2) Quotient of powers property = x 2y 8 – Simplify exponent. = y 8 x 2 Negative exponent property 16

17
**Simplify the expression. ANSWER**

Checkpoint Simplify Algebraic Expressions Simplify the expression. ANSWER 5. ( )3 2p p 4 8p 7 6. xy 4 – x 5y 3 x 4y 7 27b 2 7. ( )3 3b – 2 b 8 – s r 2 4 3 1 r 6s 12 8.

18
Homework: 6.1 p.299 #8-34 even Disregard direction that says. “Tell which properties you used”

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