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Multiplying and Dividing Monomials

Multiplying and Dividing Monomials. Objectives:. Understand the concept of a monomial Use properties of exponents to simplify expressions. 5, -21, 0. 2x, 4ab 2 , -7m 3 n 8. Monomial. An expression that is either:. a constant. a variable. a product of a constant and 1 or

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Multiplying and Dividing Monomials

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  1. Multiplying and Dividing Monomials

  2. Objectives: • Understand the concept of a monomial • Use properties of exponents to simplify expressions

  3. 5, -21, 0 2x, 4ab2, -7m3n8 Monomial An expression that is either: • a constant • a variable • a product of a constant and 1 or • more variables

  4. Multiply (a3b4)(a5b2) (a3a5)(b4b2) Group like bases Which property was applied? Commutative Property Answer: a8b6 When multiplying, add the exponents.

  5. Multiply (5a4b3)(2a6b5)

  6. Multiply (5a4b3)(2a6b5) Multiply the coefficients

  7. Multiply (5a4b3)(2a6b5) 10(a4b3)(a6b5) Multiply the coefficients Group like bases 10(a4a6)(b3b5) Answer: 10a10b8 When multiplying, add the exponents.

  8. Try This! 1. (a2b3)(a9b) Answer: a11b4 2. (3a12b4)(-5ab2)(a3b8) Answer: -15a16b14

  9. a7 a4 b5 b1 • Divide a7b5 a4b Group like bases When dividing, subtract the exponents (a7 - 4)(b5 - 1) Answer: a3b4

  10. -30 -5 Divide -30x3y4 -5xy3 Divide the coefficients. Group like bases (x3 - 1)(y4 - 3) Answer: 6x2y

  11. 2 -3 2mn2 - 3 Answer: 2 - 3 = mn2 Divide 2m5n4 -3m4n2 Divide the coefficients. Group like bases (m5 - 4)(n4 - 2)

  12. 2. - 3x10y7 6x9y2 - 3 6 - xy5 2 Answer: -1 2 = xy5 Try This! 1. m8n5 m4n2 (m8 - 4)(n5 - 2) (x10 - 9)(y7 - 2) Answer: m4n3

  13. Power of a Product (ab)2 (ab)3 (ab)(ab)(ab) (ab)(ab) (aaa)(bbb) (aa)(bb) a3b3 a2b2 Rule 4: (xy)n = xnyn Multipy the exponent outside the () times each exponent inside the ().

  14. Power of a Product (a9b5)3 (4m11n20)2 (41m11n20)2 (a9•3)(b5•3) (41•2)(m11•2)(n20•2) Answer: a27b15 Answer: 16m22n40 Rule 4: (xy)n = xnyn

  15. x y x y x y x y x4 y4 = • • • n xn yn x y = Rule 5: 4 x y

  16. Try This! 1. (2a4)3 2. (4xy5z2)4 (41x1y5z2)4 (21a4)3 (21•3)(a4•3) (41•4)(x1•4)(y5•4)(z2•4) Answer:8a12 Answer:256x4y20z8 Rule 4: (xy)n = xnyn

  17. Homework p. 466 - 467 #5, 6 - 36 even, 39, 40

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