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Evaluating Algebraic Expressions 4-4 Multiplying and Dividing Monomials Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

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Evaluating Algebraic Expressions 4-4 Multiplying and Dividing Monomials Warm Up Write in exponential form. 1. 6 · 6 · 6 · 6 · 6 2. 3x · 3x · 3x · 3x Simplify. 3. 3 4 4. (–3) 5 5. (2 4 ) 5 6. (4 2 ) 0 6565 (3x) 4 81 –243 2 20 1

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Evaluating Algebraic Expressions 4-4 Multiplying and Dividing Monomials AF2.2 Multiply and divide monomials; extend the process of taking powers and extracting roots to monomials when the latter results in a monomial with an integer exponent. Also covered: AF1.3 California Standards

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Evaluating Algebraic Expressions 4-4 Multiplying and Dividing Monomials A monomial is a number or a product of numbers and variables with exponents that are whole numbers. 7x 5, 3a 2 b 3, n 2, 8, z4z4 Monomials Not monomials m3,4z 2.5, 5 + y,, 2 x 8w38w3 To multiply two monomials, multiply the coefficients and add the exponents that have the same base.

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Evaluating Algebraic Expressions 4-4 Multiplying and Dividing Monomials Multiply. Additional Example 1: Multiplying Monomials A. (3a 2 )(4a 5 ) (3 4)(a 2 a 5 ) 12a 7 Multiply coefficients. Add exponents that have the same base. B. (4x 2 y 3 )(5xy 5 ) (4 5)(x 2 x)(y 3 y 5 ) Multiply coefficients. Add exponents that have the same base. Use the Comm. and Assoc. Properties. 3 4 a 2 + 5 (4 5)(x 2 x 1 )(y 3 y 5 ) 4 5 x 2 + 1 y 3+5 20x 3 y 8 Use the Comm. and Assoc. Properties. Think: x = x 1.

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Evaluating Algebraic Expressions 4-4 Multiplying and Dividing Monomials Multiply. Additional Example 1: Multiplying Monomials C. (–3p 2 r)(6pr 3 s) (–3 6)(p 2 p)(r r 3 )(s) Multiply coefficients. Add exponents that have the same base. –3 6 p 2 + 1 r 1+3 s –18p 3 r 4 s Use the Comm. and Assoc. Properties. (–3 6)(p 2 p 1 )(r 1 r 3 )(s)

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Evaluating Algebraic Expressions 4-4 Multiplying and Dividing Monomials Multiply. Check It Out! Example 1 A. (2b 2 )(7b 4 ) (2 7)(b 2 b 4 ) 14b 6 Multiply coefficients. Add exponents that have the same base. Use the Comm. and Assoc. Properties. 2 7 b 2 + 4 B. (4n 4 )(5n 3 )(p) (4 5)(n 4 n 3 )(p) 20n 7 p Multiply coefficients. Add exponents that have the same base. Use the Comm. and Assoc. Properties. 4 5 n 4 + 3 p

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Evaluating Algebraic Expressions 4-4 Multiplying and Dividing Monomials Multiply. Check It Out! Example 1 C. (–2a 4 b 4 )(3ab 3 c) (–2 3)(a 4 a)(b 4 b 3 )(c) Multiply coefficients. Add exponents that have the same base. –2 3 a 4 + 1 b 4+3 c –6a 5 b 7 c Use the Comm. and Assoc. Properties. (–2 3)(a 4 a 1 )(b 4 b 3 )(c)

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Evaluating Algebraic Expressions 4-4 Multiplying and Dividing Monomials To divide a monomial by a monomial, divide the coefficients and subtract the exponents of the powers in the denominator from the exponents of the powers in the numerator that have the same base.

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Evaluating Algebraic Expressions 4-4 Multiplying and Dividing Monomials Divide. Assume that no denominator equals zero. A. Divide coefficients. Subtract exponents that have the same base. Additional Example 2: Dividing Monomials 15m 5 3m 2 m 5-2 15 3 5m35m3 B. Divide coefficients. Subtract exponents that have the same base. 18a 2 b 3 16ab 3 a 2-1 b 3-3 9898 a 9898

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Evaluating Algebraic Expressions 4-4 Multiplying and Dividing Monomials Divide. Assume that no denominator equals zero. A. Divide coefficients. Subtract exponents that have the same base. Check It Out! Example 2 18x 7 6x 2 x 7-2 18 6 3x53x5 B. Divide coefficients. Subtract exponents that have the same base. 12m 2 n 3 9mn 2 m 2-1 n 3-2 4343 mn 4343

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Evaluating Algebraic Expressions 4-4 Multiplying and Dividing Monomials To raise a monomial to a power, you must first understand how to find a power of a product. Notice what happens to the exponents when you find a power of a product. (xy) 3 = xy xy xy = x x x y y y = x 3 y 3

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Evaluating Algebraic Expressions 4-4 Multiplying and Dividing Monomials Simplify. Additional Example 3: Raising a Monomial to a Power A. (3y) 3 3 3 y 3 27y 3 Raise each factor to the power. B. (2a 2 b 6 ) 4 2 4 (a 2 ) 4 (b 6 ) 4 16a 8 b 24 Raise each factor to the power. Multiply exponents.

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Evaluating Algebraic Expressions 4-4 Multiplying and Dividing Monomials Simplify. Check It Out! Example 3 A. (4a) 4 4 4 a 4 256a 4 Raise each factor to the power. B. (–3x 2 y) 2 (–3) 2 (x 2 ) 2 (y) 2 9x4y29x4y2 Raise each factor to the power. Multiply exponents.

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Evaluating Algebraic Expressions 4-4 Multiplying and Dividing Monomials Lesson Quiz Multiply. 1. (3g 2 h 3 )(–6g 7 h 2 ) 2. (12m 3 )(3mp 3 ) Divide. Assume that no denominator equals zero. 3. 4. 5. 36m 4 p 3 –18g 9 h 5 2a4b32a4b3 3 2 x –5p 3 6a6b43a2b6a6b43a2b 9x3y6x2y9x3y6x2y 20p 5 q –4p 2 q Simplify. 6.(–5y 7 ) 3 7. (3c 2 d 3 ) 4 8. (3m 2 n) 5 81c 8 d 12 –125y 21 243m 10 n 5

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