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Warm Up

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. Section 4.4. Multiplying and Dividing Monomials. California Standards.

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Warm Up

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  1. 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

  2. Section 4.4 Multiplying and Dividing Monomials

  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 Words to Know A monomial is a number or a product of numbers and variables with exponents that are whole numbers.

  5. Multiplying Monomials 1. Multiply just the coefficients first. 2. Add the exponents that have the same base. 2 + 5 12 a 7 It’s that easy!! 12a

  6. Multiplying Monomials 20x3y8 1. (4x2y3)(5xy5) 1. Multiply just the coefficients first. 2. Add the exponents that have the same base. 2. (–3p2r)(6pr3s) –18p3r4s

  7. Try on your own….. Multiply. A. (2b2)(7b4) 14b6 B. (4n4)(5n3)(p) 20n7p C. (–2a4b4)(3ab3c) –6a5b7c

  8. Dividing Monomials 1. Divide just the coefficients first. 15m5 3m2 2. Subtract the exponents that have the same base. 5 - 2 5 m 3 = 5m Great work!

  9. 9 8 4 3 a mn Dividing Monomials 1. 18a2b3 16ab3 2. 18x7 6x2 3x5 12m2n3 9mn2 3.

  10. 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

  11. Raising a monomial to a power… Simplify. A. (3y)3 27y3 33 ∙ y3 B. (2a2b6)4 16a8b24 24 ∙ (a2)4 ∙ (b6)4

  12. Try on your own…. A. (4a)4 256a4 B. (–3x2y)2 9x4y2

  13. Summary When multiplying a monomial, remember to add the exponents. When dividing monomials, remember to subtract the exponents.

  14. Lesson Quiz Multiply. 1. (3g2h3)(–6g7h2) 2. (12m3)(3mp3) Divide. Assume that no denominator equals zero. 3.4.5. –18g9h5 36m4p3 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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