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5.4 Exponent Rules and Multiplying Monomials 1. Multiply monomials. 2. Multiply numbers in scientific notation. 3. Simplify a monomial raised to a power. Objective 1 Multiply monomials. 23 • 2 4 23 means three 2s. 23 222 27 24 2222 24 means four 2s. Since there are a total of seven 2s multiplied, we can express the product as 27. Keep the base and add the exponents Product Rule for Exponents If a is a real number and m and n are integers, then am • an = am+n. Multiply: 2 9 9 5 4 6 3 3 97 310 When an equation in one variable is solved the answer is a point on a line. 4 2 4 6 4 8 3 3 4 48 5 39 39 3 5 2a 7a 14a 8 Multiplying Monomials 1. Multiply coefficients. 2. Add the exponents of the like bases. 3. Write any unlike variable bases unchanged in the product. Simplify: 3 5x 7 x 2 2 4 5 3 35x 25 81 2025 5 2x3 5x3 3 a line. When an equation in one variable is solved the answer3is a point on 2 x 5x 10x 6 1 2 5 3 2 5 k m km n k 4 6 3 7x 3 5 8 4 k m n 36 Objective 2 Multiply numbers in scientific notation. Monomials: Scientific notation: 4a3 2a6 4 2a36 3 6 3 6 4 10 2 10 4 2 10 8a9 8 109 Multiply and write result in scientific notation: 3 4 4.5 10 5.7 10 25.65 107 2.565 108 When an equation in one variable is solved the answer is a point on a line. 3 6 6.2 10 3.1 10 19.22 10 3 1.922 10 2 Objective 3 Simplify a monomial raised to a power. x 2 5 2 2 2 2 x x x x x 2 x 10 A Power Raised to a Power If a is a real number and m and n are integers, then (am)n = amn. 4a 3 4a 4a 4a 4 3 a 3 64a3 Raising a Product to a Power If a and b are real numbers and n is an integer, then (ab)n = anbn. 2x y 3 2 4 4 12 8 12 8 2 x y 16x y Simplifying a Monomial Raised to a Power 1. Evaluate the coefficient raised to that power. 2. Multiply each variable’s exponent by the power. Simplify: 3x y 2 32 2 3 5 2x y 2 x 10 y 15 9x 4 y 6 When an equation in one variable is solved the answer is a point on a line. x y 2 x y 2 3 2 5 x4y2 x 15 y 10 Simplify: 2x y 2xy 2 4 23 3x4y2z yz4 2 4 x 8 y 4 23 x 3 y 6 27 x 11 y 10 128 x 11 y 10 When an equation point6on3a line 5 . 20 3 in one 5variable is solved the answer 3is a 12 3 x y z y z 33 x 12 y 11 z 23 27 x 12 y 11 z 23 x y x y 5 23 2 32 x 15 y 6 x 4 y 6 x 19 y 12 7 3 6 b 3 b Simplify. a) 18b 21 b) 18b10 c) 9b 21 d) 9b10 5.4 Copyright © 2011 Pearson Education, Inc. Slide 5- 17 7 3 6 b 3 b Simplify. a) 18b 21 b) 18b10 c) 9b 21 d) 9b10 5.4 Copyright © 2011 Pearson Education, Inc. Slide 5- 18 Simplify. 4 y 2 5 y 3 4 a) 20 y 9 b) 20 y 20 c) 2500 y 9 d) 2500y14 5.4 Copyright © 2011 Pearson Education, Inc. Slide 5- 19 Simplify. 4 y 2 5 y 3 4 a) 20 y 9 b) 20 y 20 c) 2500 y 9 d) 2500y14 5.4 Copyright © 2011 Pearson Education, Inc. Slide 5- 20