#### Transcript Chapter 8

~ Chapter 8 ~ Exponents & Exponential Functions Lesson 8-1 Zero & Negative Exponents Lesson 8-2 Scientific Notation Lesson 8-3 Multiplication Properties of Exponents Lesson 8-4 More Multiplication Properties of Exponents Lesson 8-5 Division Properties of Exponents Chapter Review Zero & Negative Exponents Cumulative Review Chap 1-7 Zero & Negative Exponents Notes Zero as an exponent For every nonzero number a, a 50 = 1 ( - 8)0 = 1 0 = 1… 53,4280 = 1 (1/5)0 = 1 Negative Exponents For every nonzero number a and integer n, a-n = 1/an 10-5 = 1/105 (-6)-9 = 1/(-6)9 x-7 = ? Simplifying a power 3-4 = 1/34 = 1/81 (-7)0 = 1 (-4)-3 = 1/(-4)3 = 1/(-64) 7-1 = 1/71 = 1/7 An algebraic expression is written in simplest form when it is written with only positive exponents. Simplifying an Exponential Expression 4yx-3 = 4y/x3 11m-5 = 7x-4t2 = 2/a-3 = n-5/v2 = Zero & Negative Exponents Notes Evaluating an Exponential Expression 3m2t-2 for m = 2 and t = -3 3m2/t2 = 3(2)2/(-3)2 = 3(4)/9 = 12/9 = 1 1/3 Evaluate the following for n = -2 & w = 5 n-3w0 = w0/n3 = 50/(-2)3 = 1/(-8) = - 1/8 n-1/w2 = 1/n1w2 = 1/(-2)1 (5)2 = 1/(-2*25) = - 1/50 1/nw-2 = w2/n = (5)2/(-2) = 25/(-2) = -12 1/2 Zero & Negative Exponents Homework Homework – Practice 8-1 odd Scientific Notation Practice 8-1 Scientific Notation Practice 8-1 Scientific Notation Notes Scientific Notation Format – has one nonzero digit to the left of the decimal point multiplied by 10 raised to a power. Form: a x 10n, where n is an integer and 1 ≤ a < 10. Determine if the following numbers are written in scientific notation… 3.42 x 10-7 52 x 104 0.04 x 10-5 Writing a number in scientific notation… Step 1: Move the decimal until there is one nonzero digit to the left of the decimal place. Step 2: Count the number of places the decimal was moved (this is the power of 10) (If decimal was moved to the left, the power is positive. If the decimal was moved to the right, the power is negative.) Step 3: Drop any unneeded zeros. 267,000 = 0.00000000009 = 46,205,000 = 0.0000325= Scientific Notation Notes Writing a Number in Standard Notation Positive power – move the decimal to right. (value is greater than 1) Negative power – move the decimal to the left. (value is less than 1) 3.2 x 1012 = 3,200,000,000,000 5.07 x 104 = 5.6 x 10-4 = 0.00056 8.3 x 10-2 = 50,700 0.083 Ordering numbers using Scientific Notation Step 1: Write each number in scientific notation Step 2: Order the powers of 10. Arrange the decimals with the same power of 10 in order. Step 3: Write the original numbers in order… Order from least to greatest: 60.2 x 10-5, 63 x 104, 0.067 x 103, and 61 x 10-2 6.02 x 10-4 , 6.1 x 10-1, 6.7 x 101, 6.3 x 105 so… Scientific Notation Notes Multiplying a number in Scientific Notation 2.5(6 x 103) = (2.5 x 6) x 103 = 15 x 103 = 1.5 x 104 0.4(2 x 10-9) = 8(7 x 10-3) = 0.2(3 x 102) = Scientific Notation Homework Homework ~ Practice 8-2 even Multiplication Properties of Exponents Practice 8-2 Multiplication Properties of Exponents Practice 8-2 Multiplication Properties of Exponents Notes Multiplying powers with the Same Base For every nonzero number a and integers m and n, am * an = am + n 53 * 5 6 = 24 * 2-3 = 7-3 * 72 * 76 = a * a5 = x * x4 * x3 = n2 * n3 * 7n = 6y2 * 3y3 *2y-4 = More multiplying powers in an Algebraic Expression a * b * a5 = 2y3 * 7x2 * 2y4 = m2 * n-2 *7m = Multiplying Numbers in Scientific Notation (2.5 x 108)(6 x 103) = (2.5 x 6)(108 x 103) = 15 x 1011 = 1.5 x 1012 (1.5 x 10-2)(3 x 104) = (9 x 10-6)(7 x 10-9) = Multiplication Properties of Exponents Homework Homework – Practice 8-3 odd More Multiplication Properties of Exponents Practice 8-3 More Multiplication Properties of Exponents Practice 8-3 More Multiplication Properties of Exponents Notes Raising a Power to a Power For every nonzero number a and integers m & n, (am)n = amn (58)3 = (n-2)6 = (xy5)9 = Remember to simplify… (a4)7 = (a-4)7 = Simplifying an Expression with Powers (n4)3 * n5 = t2(t7)-2 = (a4)2 * (a2)5 = Raising a Product to a Power For every nonzero number a and b and integer n, (ab)n = anbn (5x3)6 = (8y7)4 = Simplifying a Product Raised to a power (6x4y2)-3 = (4g5)-2 = (3t0)4 = More Multiplication Properties of Exponents Notes (x-2)2(3xy2)4 = x-2*2(34x4y2*4) = x-4(34x4y8) = (c2)3(3c5)4 = (2a3)5(3ab2)3 = (6mn)3(5m-3)2 = Scientific Notation raised to a Power (2 x 108)4 = 10-3(3 x 105)3 = 34x-4+4y8 = 81x0y8 = 81y8 More Multiplication Properties of Exponents Homework Homework – Practice 8-4 odd Division Properties of Exponents Practice 8-4 Division Properties of Exponents Practice 8-4 Division Properties of Exponents Notes Dividing Powers with the Same Base For every nonzero number a and integers m & n, am = am-n an a6 = a15 c-2d9 = c9 d 7 x6y-5z4 = x4y-2z-2 Dividing numbers in Scientific Notation 2 x 103 = 8 x 108 7.5 x 1012 = 2.5 x 10-4 4.2 x 10-7 = 12.6 x 10-2 Raising a Quotient to a Power For every nonzero number a & b and integer n, (a/b)n = an bn (3/x2)2 = (a/b)-n = a-n = b-n (x/y2)4 = bn an (t7/23)2 = Division Properties of Exponents Notes Simplifying an Exponential Expression (3/4)-3 = (4/3)3 = (-1/2)-5 = (2/-1)5 = (2r/s)-1 = (s/2r)1 = (7a/m)-2 = (m/7a)2 = Division Properties of Exponents Homework Homework ~ Practice 8-5 odd Division Properties of Exponents Practice 8-5 Division Properties of Exponents Practice 8-5 ~ Chapter 8 ~ Chapter Review ~ Chapter 8 ~ Chapter 8 Extra Pr (2) 5/m3 (4) m14/t10 (6) w6j22 (8) 9n8 (10) a4 (14) 2t8 (16) 1/c12 (18) 1/9 (12) 6t4 (20) 144 (26) 6.3 x 10 -4 (24) -64/27 (28) 2 x 10 -4 (30) 6.2 x 109 (32) 8.91 x 10 -10 (38) 63,000 (22) 16 (34) 0.00000032 (40) 5295.6 (36) 0.000425