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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. Warm Up Write in exponential form. 1. 6 · 6 · 6 · 6 · 6 2. 3 x · 3 x · 3 x · 3 x Simplify. 3. 3 4 4. (–3) 5 5. (2 4 ) 5 6. (4 2 ) 0. 6 5. (3 x ) 4. 81. – 243. 2 20. 1. California Standards.

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

  2. Warm Up Write in exponential form. 1.6 · 6 · 6 · 6 · 6 2. 3x · 3x · 3x · 3x Simplify. 3. 34 4. (–3)5 5. (24)5 6.(42)0 65 (3x)4 81 –243 220 1

  3. California Standards 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

  4. z 4 7x5, -3a2b3, n2, 8, 8w3 m-3,4z2.5, 5 + y, , 2x A monomial is a number or a product of numbers and variables with exponents that are whole numbers. To multiply two monomials, multiply the coefficients and add the exponents that have the same base.

  5. Additional Example 1: Multiplying Monomials Multiply. A. (3a2)(4a5) Use the Comm. and Assoc. Properties. (3 ∙4)(a2 ∙ a5) Multiply coefficients. Add exponents that have the same base. 3 ∙4 ∙ a2 +5 12a7 B. (4x2y3)(5xy5) Use the Comm. and Assoc. Properties. Think: x = x1. (4 ∙ 5)(x2∙ x)(y3 ∙ y5) (4 ∙ 5)(x2∙ x1)(y3 ∙ y5) Multiply coefficients. Add exponents that have the same base. 4 ∙ 5 ∙ x2 + 1∙ y3+5 20x3y8

  6. Additional Example 1: Multiplying Monomials Multiply. C. (–3p2r)(6pr3s) Use the Comm. and Assoc. Properties. (–3 ∙ 6)(p2∙ p)(r ∙ r3)(s) (–3 ∙ 6)(p2∙ p1)(r1 ∙ r3)(s) Multiply coefficients. Add exponents that have the same base. –3 ∙ 6 ∙ p2 + 1∙ r1+3 ∙ s –18p3r4s

  7. Check It Out! Example 1 Multiply. A. (2b2)(7b4) Use the Comm. and Assoc. Properties. (2 ∙7)(b2 ∙ b4) Multiply coefficients. Add exponents that have the same base. 2 ∙7 ∙ b2 +4 14b6 B. (4n4)(5n3)(p) Use the Comm. and Assoc. Properties. (4 ∙5)(n4 ∙ n3)(p) Multiply coefficients. Add exponents that have the same base. 4 ∙5 ∙ n4 +3 ∙ p 20n7p

  8. Check It Out! Example 1 Multiply. C. (–2a4b4)(3ab3c) Use the Comm. and Assoc. Properties. (–2 ∙ 3)(a4 ∙ a)(b4 ∙ b3)(c) (–2 ∙ 3)(a4 ∙ a1)(b4 ∙ b3)(c) Multiply coefficients. Add exponents that have the same base. –2 ∙ 3 ∙ a4 + 1 ∙ b4+3 ∙ c –6a5b7c

  9. 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. 15 3 m5-2 9 8 a2-1 b3-3 9 8 a Additional Example 2: Dividing Monomials Divide. Assume that no denominator equals zero. 15m5 3m2 A. Divide coefficients. Subtract exponents that have the same base. 5m3 18a2b3 16ab3 B. Divide coefficients. Subtract exponents that have the same base.

  11. 18 6 x7-2 4 3 m2-1 n3-2 4 3 mn Check It Out! Example 2 Divide. Assume that no denominator equals zero. 18x7 6x2 A. Divide coefficients. Subtract exponents that have the same base. 3x5 12m2n3 9mn2 B. Divide coefficients. Subtract exponents that have the same base.

  12. 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 = x3y3

  13. Additional Example 3: Raising a Monomial to a Power Simplify. A. (3y)3 33 ∙ y3 Raise each factor to the power. 27y3 B. (2a2b6)4 24 ∙ (a2)4 ∙ (b6)4 Raise each factor to the power. Multiply exponents. 16a8b24

  14. Check It Out! Example 3 Simplify. A. (4a)4 44 ∙ a4 Raise each factor to the power. 256a4 B. (–3x2y)2 (–3)2 ∙ (x2)2 ∙(y)2 Raise each factor to the power. Multiply exponents. 9x4y2

  15. Lesson Quiz Multiply. 1. (3g2h3)(–6g7h2) 2. (12m3)(3mp3) Divide. Assume that no denominator equals zero. 3.4.5. 36m4p3 –18g9h5 6a6b4 3a2b 9x3y 6x2y 3 2 x 20p5q –4p2q 2a4b3 –5p3 Simplify. 6.(–5y7)3 7. (3c2d3)4 8. (3m2n)5 –125y21 81c8d12 243m10n5

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