Lesson 3: Properties of Exponents
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1 Lesso : Properties of Expoets Topics d Objectives: Properties of Expoets o Zero d Oe o The Multiplictio Property o Power to Power o Power of Product Multiplictio of Polyomils o Multiplyig Moomils o The Distributive Property o Multiplictio of Polyomils o Squrig Biomil Divisio Properties of Expoets o The Divisio Property o Risig Quotiet to Power Negtive Expoets Divisio of Polyomils Scietific Nottio o Powers of te o Writig umbers i scietific ottio d stdrd form
2 Itroductory Algebr
3 Itroductory Algebr Properties of Expoets Give y rel umbers, b, c, m, d 1 = 1 = 0 = 0 = 0 0 Exmple 1: Evlute d simplify the followig expressios. Assume x 0, 0, b 0, d c 0. 5x 0 = (x + 1) 0 = 0 + b 0 + c 0 = The Multiplictio Property: m m Exmple : Simplify the followig expressios 9 = b 5 b 4 b= 5x y 5 (7xy 9 )= Risig Power to Power: ( m ) m Exmple : Simplify the followig expressios (x ) 9 = 5b (b 5 ) 8 =
4 Itroductory Algebr Risig Product to Power: ( b) b Exmple 4: Simplify the followig expressios (5x) = (x y ) 9 = ( 8b 5 ) = 5( w 7 ) = 5 4 ( ) = You Try 1. Simplify the followig expressios. 4 ( x ) b. x( x ) c. 4 5 g g g d. 0
5 Itroductory Algebr Multiplictio of Polyomils Multiplictio of Moomils Exmple 1: Multiply d simplify. (x 5 )( x 9 ) = Exmple : Expd d simplify. The Distributive Property 5x (x 5 4x x + 8)= Exmple : Multiply d simplify.. (x + )(x + 4) = Multiplictio of Polyomils b. (m 5)(m 6) = c. (d 4)(d + 5) = d. (x )(x + x 4) =
6 Itroductory Algebr Exmple 4: Multiply d simplify. Squrig Biomil. ( + 5) b. ( ). Multiply d simplify. You Try. x (x 5 + 6x 5x)= b. (x 4)(5x + )= c. (p 5) =
7 Itroductory Algebr Applictios from Geometry Exmple 1: Write polyomil i simplest form tht represets the re of the squre. SOLUTION: The blue squre hs re: The yellow squre hs re: The pik rectgles ech hve re: Totl Are = = Exmple 1 (other wy): Write polyomil i simplest form tht represets the re of the squre. SOLUTION: The totl legth of ech side is x + y. Totl Are = (x + y)( x + y) = x + xy + yx + y Note tht xy d yx re like terms: xy + yx = xy Totl Are = x + xy + y Exmple : Write polyomil i simplest form tht represets the re of the shded regio. SOLUTION: To fid the re of the shded regio we fid the re of the big squre d subtrct the re of the little squre. The big squre hs re: The little squre hs re: Are of the shded regio
8 Itroductory Algebr You Try. Write polyomil i simplest form tht represets the totl re of the figure show below. 4. Write polyomil i simplest form tht represets the re of the drk blue regio of the figure show below.
9 Itroductory Algebr Divisio Properties of Expoets m The Divisio Property: 0 m Exmple 1: Simplify the followig expressios 50 x 10 4 b 4 x 6b 5 Risig Quotiet to Power: b 0 b b Exmple : Simplify the followig expressios x 4t 7 y 6 u 5. Simplify the followig expressios. You Try = b. 8 6xy = 5 9xy
10 Itroductory Algebr
11 Itroductory Algebr Negtive Expoets For y rel umbers 0, b 0, d m: b m b m m 1 1 m m m Exmple 1: Rewrite ech of the followig with oly positive expoets 1. x = b. = x c. = d. 4 5 = e. 4 x = f. ( ) 4 x = Exmple : Simplify the followig expressios. Write your swer with oly positive expoets.. 4 p p p b. 5 b c c. d d 7 = d. 10 4t u = 1 6t u
12 Itroductory Algebr You Try 6. Simplify the followig expressios. Write your swers with oly positive expoets 7. b. 8 = c. 4 6wx wx = d. ( x )
13 Itroductory Algebr Divisio of Polyomils Simplify the followig expressios. Write your swer with oly positive expoets. Exmple 1: 6w 0w 8 Exmple : x 6 Exmple : 6x x 4 4x Exmple 4:
14 Itroductory Algebr You Try 7. Simplify the followig expressios. Write your swer with oly positive expoets.. 11x 15 = b. x 5x 1 x =
15 Itroductory Algebr Scietific Nottio Scietific ottio is the wy tht scietists esily hdle very lrge umbers or very smll umbers. For exmple, isted of writig , we write 5.6 x Powers of Te Scietific Nottio Stdrd Form ,000.1 x 10 4 =, ,000.1 x 10 =, x 10 = x 10 1 = x 10 0 = x 10-1 = x 10 - = x 10 - = x 10-4 = Writig Numbers i Scietific Nottio d Stdrd Form Scietific Nottio Stdrd Form.1 x 10 4,100.1 x Exmple 1: Write the followig umbers i stdrd form x 10 5 = b. 8. x 10-7 =
16 Itroductory Algebr Exmple : Write the followig umbers i scietific ottio.. 8,140,000 = b = O Your Clcultor Exmple : Evlute the followig o your clcultor. Write i stdrd form = b = You Try 8. Write the followig umbers i stdrd form x 10 5 = b. 1.5 E - = 9. Write the followig umbers i scietific ottio = b. 5,40,000,000 =
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