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Do Now 2/1/10 Copy Text HW in your planner. p. 492, #10-48 evens In your notebook, complete the “Investigating Algebra” Activity on page 488 in the text. Copy and complete both tables and then answer the Draw Conclusions problems #1-8. You will have 10 minutes to finish. Chapter 8 “Exponents and Exponential Functions” (8.1) Exponents involving products (8.2) Exponents involving quotients (8.3) Zero and negative exponents (8.4) Scientific notation Objective SWBAT use properties of exponents involving products POWER an expression that represents repeated multiplication. 2 4 EXPONENT BASE Product 2222 Words two to the fourth power GUIDED PRACTICE Evaluate the expression. 1. x3 when x = 8 2. k3 when k = 2.5 3. d4 when SOLUTIONS 1. x3 = 83 =8 8 8 = 512 2. k3 = 2.53 = (2.5)(2.5)(2.5) = 15.625 3. d4 = 1 3 4 ( ) 1 = 3 = 1 81 1 3 1 3 1 3 d= 1 3 Section 8.1, “Apply Exponent Properties Involving Products” (1) Product of Powers Property a a a m n 5 5 5 6 3 63 5 9 (2) Power of a Power Property (a ) a m m n n mn (34 )3 343 312 (3) Power of a Product Property (ab) m a mb m (23 17)5 235 175 Try It Out... (1) Product of Powers Property a a4 a7 a a a 1 a 4 7 1 4 7 a12 (7) (7) 3 ( 7 ) ( 7 ) 3 ( 7 ) 31 ( 7 ) 4 1 Try It Out... (2) Power of a Power Property 3 8 (n ) n 38 n 24 4 3 [(4) ] [( x 3) ] 5 2 43 ( x 3) 12 ( x 3) (4) (4) 52 10 Try It Out... (3) Power of a Product Property (4 8) 7 (8c) 4 8 7 2 ( 8 c ) 2 ( 8) 2 c 2 7 64c (9 xy) (8c) 2 (9 x y ) 2 9 x y 2 2 81x 2 y 2 2 2 2 (8 c ) 2 (8) 2 c 2 64c 2 Order of Magnitude the power of 10 nearest to the quantity **HINT** Think of the order of magnitude as rounding to the closest power of 10. There are about 91,000 species of insect in the United States. What is the order of magnitude of the amount of insects in the United States? The power of 10 closest to 91,000 is 100,000 or 10 to the 5th power. Try It Out... Use All Three Properties (2 x ) x 3 2 2 (x ) x 4 2 3 2 4 x x 6 4 4 4 x10 Challenge (3x y) (11x y ) 2 3 3 5 2 (27 x y )(121x y ) 6 3 3267 x y 12 13 6 10 Homework Prerequisite Skills Text p. 486, #1-13 all 1) exponent: 8, base: 13 2) power 3) 100 4) 27 5) 25/36 6) 1/8 7) 6.01, 6.12, 6.2 8) 0.0098, 0.073, 0.101 9) 0.04 10) 0.005 11) 0.138 12) 1.45 13) f(x) = x + 2