University:
Montgomery College
Course:
MATH 130: Elements of Mathematics I: Mathematical Reasoning and Number Systems
Academic year:

2023
Views:

485

Pages:

1
Author:

levedzgetmo7f

Mini-Lecture 5.1 Exponents Learning Objectives: 1. Evaluate exponential expressions. 2. Use the product rule for exponents. 3. Use the power rule for exponents. 4. Use the power rule for products and quotients. 5. Use the quotient rule for exponents, and define a number raised to the 0 power. 6. Decide which rule(s) to use to simplify an expression. Examples: 1. Evaluate each expression. a) 33 b) (-7)2 c) -62 d) -4y2 when y = -5 2. Use the product rule to simplify each expression. Write the results using exponents. a) x5 · x3 b) (4z3)(9z5) c) (-3x3y2)(-5x4y6) d) (9ab2c4)(-11a3b)(-2b2c5) 3. Use the power rules to simplify each expression. a) (x7)3 b) (y3)11 c) (xy)5 d) (5x3y2z)3 4. Use the power rule for products and quotients. 3 3 2 a) (-7a b ) ⎛ ab ⎞ b) ⎜ ⎟ ⎝ c ⎠ 7 ⎛ −3xy ⎞ c) ⎜ ⎟ ⎝ z3 ⎠ ⎛ 3x 2 y 4 d) ⎜ ⎜ −2 z 3 ⎝ 4 ⎞ ⎟ ⎟ ⎠ 2 5. Use the quotient rule and simplify each expression. a) x5 x2 b) (−6)11 c) ( −6 )9 x12 y 5 d) x8 y 4 8a3b8c3 18ab5c 2 Simplify each expression. ⎛3⎞ f) ⎜ ⎟ ⎝7⎠ e) 80 0 g) (5x2y)0 h) x0 + 90 6. Mixed practice. Decide which rules to use and simplify each expression. 3 2 0 2 a) (8a b c ) ⎛ −3 x 2 y 5 ⎞ b) ⎜ ⎟ ⎜ 2 xz 2 ⎟ ⎝ ⎠ 3 2 3 3 2 7 c) (-4a c )(-6a b c ) d) (12ab )4 ( 6a 2b 2 ) 2 Teaching Notes: • Most students need a lot of practice to master these rules. • Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) 27; 1b) 49; 1c) -36; 1d) -100; 2a) x8; 2b) 36z8; 2c) 15x7y8; 2d) 198a4b5c9; 3a) x21; 3b) y33; a 7b7 81x 4 y 4 9 x 4 y8 ; 4c) ; 4d) ; 5a) x3; 5b) 36; 5c) x4y; 7 12 6 c z 4z 2 3 4 15 4a b c −27 x y ; 5e) 1; 5f) 1; 5g) 1; 5h) 2; 6a) 64a6b4; 6b) ; 6c) 24a5b2c10; 6d) 576 5d) 6 9 4z 3c) x5y5; 3d) 125x9y6z3; 4a) 49a6b6; 4b)