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

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Presentation on theme: "Evaluating Algebraic Expressions 4-4 Multiplying and Dividing Monomials Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson."— Presentation transcript:

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

2 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

3 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

4 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.

5 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.

6 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)

7 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

8 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)

9 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.

10 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

11 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

12 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

13 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.

14 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.

15 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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