Multiplying and Dividing Monomials

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Monomials Multiplying Monomials and Raising Monomials to Powers.

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Multiplying and Dividing Monomials

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

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

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

Multiply (5a4b3)(2a6b5)

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

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

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

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

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

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

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

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

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

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

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