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Warm Up Write in exponential form. 1. 6 · 6 · 6 · 6 · 6 65 2. 3x · 3x · 3x · 3x (3x)4 Simplify. 3. 34 81 4. (–3)5 –243 5. (24)5 220 6. (42)0 1 Multiplying and Dividing Monomials Section 4.4 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 Words to Know A monomial is a number or a product of numbers and variables with exponents that are whole numbers. Monomials Not monomials z 8, 4 8 m-3,4z2.5, 5 + y, w3 , 2x 7x5, -3a2b3, n 2, Multiplying Monomials 3a 4a 2 5 1. Multiply just the coefficients first. 2. Add the exponents that have the same base. Multiplying Monomials 1. (4x2y3)(5xy5) 20x3y8 1. Multiply just the coefficients first. 2. Add the exponents that have the same base. 2. (–3p2r)(6pr3s) –18p3r4s Try on your own….. Multiply. A. (2b2)(7b4) B. (4n4)(5n3)(p) C. (–2a4b4)(3ab3c) 14b6 20n7p –6a5b7c Dividing Monomials 15m5 3m2 1. Divide just the coefficients first. 2. Subtract the exponents that have the same base. Dividing Monomials 18a2b3 16ab3 9a 8 18x7 6x2 3x5 12m2n3 9mn2 4 mn 3 Raising a monomial to a power… 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 Raising a monomial to a power… Simplify. A. (3y)3 27y3 33 ∙ y3 B. (2a2b6)4 24 ∙ (a2)4 ∙ (b6)4 16a8b24 Try on your own…. A. (4a)4 256a4 B. (–3x2y)2 9x4y2 Summary When multiplying a monomial, remember to add the exponents. When dividing monomials, remember to subtract the exponents. Lesson Quiz Multiply. 1. (3g2h3)(–6g7h2) –18g9h5 2. (12m3)(3mp3) 36m4p3 Divide. Assume that no denominator equals zero. 6b4 6a 3. 3a2b 2a4b3 3y 9x 4. 6x2y Simplify. 6.(–5y7)3 –125y21 7. (3c2d3)4 81c8d12 8. (3m2n)5 243m10n5 3 x 2 5q 20p 5. –4p2q –5p3