Multiplying and Dividing Monomials Objectives n n Understand

Multiplying and Dividing Monomials

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

Monomial An expression that is either: • a constant 5, -21, 0 • a variable • a product of a constant and 1 or 2 x, 4 ab 2, -7 m 3 n 8 more variables

Multiply (a 3 b 4)(a 5 b 2) Group like bases (a 3 a 5)(b 4 b 2) Which property was applied? Commutative Property Answer: a 8 b 6 When multiplying, add the exponents.

Multiply (5 a 4 b 3)(2 a 6 b 5)

Multiply (5 a 4 b 3)(2 a 6 b 5) Multiply the coefficients

Multiply (5 a 4 b 3)(2 a 6 b 5) Multiply the coefficients Group like bases 10(a 4 b 3)(a 6 b 5) 10(a 4 a 6)(b 3 b 5) Answer: 10 a 10 b 8 When multiplying, add the exponents.

Try This! 1. (a 2 b 3)(a 9 b) Answer: a 11 b 4 2. (3 a 12 b 4)(-5 ab 2)(a 3 b 8) Answer: -15 a 16 b 14

Divide a 7 b 5 a 4 b a 7 Group like bases a 4 When dividing, • b 5 b 1 (a 7 - 4)(b 5 - 1) subtract the exponents Answer: a 3 b 4

Divide -30 x 3 y 4 -5 xy 3 Divide the coefficients. Group like bases -30 (x 3 - 1)(y 4 - 3) -5 Answer: 6 x 2 y

Divide 2 m 5 n 4 -3 m 4 n 2 Divide the coefficients. Group like bases 2 -3 Answer: 2 -3 (m 5 - 4)(n 4 - 2) mn 2 = 2 mn 2 -3

Try This! 1. m 8 n 5 m 4 n 2 (m 8 - 4)(n 5 - 2) Answer: m 4 n 3 2. - 3 x 10 y 7 6 x 9 y 2 - 3 (x 10 - 9)(y 7 - 2) 6 Answer: -1 2 xy 5 = - xy 5 2

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

Power of a Product (a 9 b 5)3 (a 9 • 3)(b 5 • 3) Answer: a 27 b 15 (4 m 11 n 20)2 (41 • 2)(m 11 • 2)(n 20 • 2) Answer: 16 m 22 n 40 Rule 4: (xy)n = xnyn

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

Try This! 1. (2 a 4)3 2. (4 xy 5 z 2)4 (21 a 4)3 (41 x 1 y 5 z 2)4 (21 • 3)(a 4 • 3) Answer: 8 a 12 (41 • 4)(x 1 • 4)(y 5 • 4)(z 2 • 4) Answer: 256 x 4 y 20 z 8 Rule 4: (xy)n = xnyn