VIEWS: 29 PAGES: 28 POSTED ON: 1/17/2012
Warm-Up, 1 Consider the algebraic expression 3(a + 2b). We usually think of this as 3 distributed through the parenthesis, but it also means 3 copies of a + 2b: a + 2b + a + 2b + a + 2b Warm-Up, 2 Make a drawing to represent the algebraic expression 4(2a + 3b) Warm-Up, 3 Make a drawing to represent the algebraic expression (2a + 3b)4 5.1: Use Properties of Exponents Objectives: 1. To simplify numeric and algebraic expressions using the properties of exponents Vocabulary As a group, define Base Exponent each of these without your book. Scientific Notation Give an example of each word and leave a bit of space for additions and revisions. Exponents • Exponents mean Exponent repeated multiplication 2 3 = 222 Base Exercise 1 1. Write 24 in expanded form. 2. Write x3 in expanded form. 3. Simplify (23)2 4. Simplify 2x2 ÷ x Investigation 1 In this Investigation, we will (re)discover some general properties of exponents. They include the Multiplication and xy Division Properties, and Power Properties. Investigation 1: Multiplication Step 1: Rewrite each product in expanded form, and then rewrite it in exponential form with a single base. 34·32 103·106 x3·x5 a2·a4 Step 2: Compare your answers to the original product. Is there a shortcut? Step 3: Generalize your observations by filling in the blank: bm·bn = b-?- Investigation 1: Powers Step 1: Rewrite each expression without parentheses. (45)2 (x3)4 (5m)n (xy)3 Step 2: Generalize your observations by filling in the blanks: (bm)n = b-?- (ab)n = a-?-b-?- Investigation 1: Division Step 1: Write the numerator and denominator in expanded form, and then reduce to eliminate common factors. Rewrite the factors that remain with exponents. 9 3 3 4 6 5 3 5 4 x 6 2 2 3 5 3 5 4 x Step 2: Generalize your observations by filling in n the blank: b ? b m b Properties of Exponents Multiplication Power Division Property of Properties of Property of Exponents Exponents Exponents n (bm)n = bmn b nm bm·bn = bm+n (ab)n = anbn m b b Exercise 2 Practice simplifying expressions. 1. x2x5 2. (2x2y)3 m9 3. 4. a3b7 m6 Exercise 3 Simplify (3x + 2)2 Not the Power Property Notice that when expanding (3x + 2)2, you don’t get to use the Power Property of exponents to “distribute” the exponent through the parenthesis. The Power Property of Exponents only works across multiplication and division NOT addition or subtraction! Exercise 4 Evaluate the expression. 1. (42)3 2. (−8)(−8)3 3 2 3. (−325)3 4. 9 Exercise 5 Use the division property of exponents to rewrite each expression with a single exponent. Then expand each original expression and simplify. Compare your answers. 2 3 4 5 3 x 7 x 4 6 4 5 3 x 7 x Properties of Exponents Negative Exponents Zero Exponents n 1 b n b b0 = 1 1 n b n b Exercise 6 Simplify the expression. 1. 12−4 2. w5w−8w6 2 c 2 4 5 20x y z 3. 4 4. d 4 4 x yz 3 Always Look on the Bright Side of Life… When you simplify an algebraic expression involving exponents, all the exponents must be POSITIVE. n abc ab n d dc • Negative exponents in the numerator need to go in the denominator Always Look on the Bright Side of Life… When you simplify an algebraic expression involving exponents, all the exponents must be POSITIVE. n ab abc n dc d • Negative exponents in the denominator need to go in the numerator Exercise 7 Simply the expression. 6 5 3 1. x x x 2. 7y 2 z 5 y 4 z 1 3 s 2 x y 4 2 3. 4 4. 3 6 t x y Exercise 8 The radius of Jupiter is about 11 times greater than the radius of earth. How many times as great as Earth’s volume is Jupiter’s volume? 4 3 V r 3 Exercise 9 3 5 9 The area of a rectangle is 16a b c units2. Find the length of the rectangle if its width 2 3 is 2a bc units. Exercise 10 Let’s say the number c x 10n is in scientific notation. What must be true about c? What must be true about n? Scientific Notation The number c x 10n is in scientific notation when 1 ≤ c < 10 and n is an integer. • Easy to multiply, divide, and raise to powers using the properties of exponents • NOT so easy to add and subtract Exercise 11 Write the answer in scientific notation. 7.5 108 4.5 104 1. 4.2 103 1.5 10 6 2. 1.5 107 Assignment • P. 333-335: 1, 2, 3- 21 M3, 24-36 even, 39-45, 47, 50, 52, 54-56 • Further Work with Exponents Worksheet: Evens