Multiplying and Dividing Monomials CCS: A-CED.1

A-CED.1 CREATE equations and inequalities in one variable and USE them to solve problems. INCLUDE equations arising from linear and quadratic functions, and simple rational and exponential functions.

E.Q: 1-How are algebraic properties used to create expressions? 2- How do we use the “Laws of Exponents” when we multiply and divide monomials?

Mathematical Practice 1. Make sense of problems, and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments, and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for, and make use of, structure. 8. Look for, and express regularity in, repeated reasoning.

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

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

Multiply (a 3 b 4 )(a 5 b 2 ) (a 3 a 5 )(b 4 b 2 ) Group like bases Which property was applied?

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

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

Try This! 1. (a 2 b 3 )(a 9 b) 2. (3a 12 b 4 )(-5ab 2 )(a 3 b 8 )

Divide a7b5a4ba7b5a4b

-30x 3 y 4 -5xy 3

Divide 2m 5 n 4 -3m 4 n 2

Try This! 1. m 8 n 5 m 4 n x 10 y 7 6x 9 y 2

Power of a Product (ab) 2 Rule 4: (xy) n = x n y n (ab)(ab) a2b2a2b2 (ab) 3 (ab)(ab)(ab) a3b3a3b3 Multipy the exponent outside the () times each exponent inside the (). (aa)(bb) (aaa)(bbb)

Power of a Product (a 9 b 5 ) 3 Rule 4: (xy) n = x n y n (4m 11 n 20 ) 2

xyxy 4 xyxy xyxy xyxy xyxy = x4y4x4y4 Rule 5: xyxy n = xnynxnyn

Try This! 1. (2a 4 ) 3 Rule 4: (xy) n = x n y n 2. (4xy 5 z 2 ) 4