Objectives The student will be able to: 1. multiply monomials. 2. simplify expressions with monomials. SOL: A.10 Designed by Skip Tyler, Varina High School

A monomial is a 1. number, 2. variable, or 3. a product of one or more numbers and variables. Examples: 5 y 3x2y3

Why are the following not monomials? x + y addition division 2 - 3a subtraction

Multiplying Monomials When multiplying monomials, you ADD the exponents. 1) x2 • x4 x2+4 x6 2) 2a2y3 • 3a3y4 6a5y7

Simplify m3(m4)(m) m7 m8 m12 m13

Power of a Power When you have an exponent with an exponent, you multiply those exponents. 1) (x2)3 x2• 3 x6 2) (y3)4 y12

Simplify (p2)4 p2 p4 p8 p16

Power of a Product When you have a power outside of the parentheses, everything in the parentheses is raised to that power. 1) (2a)3 23a3 8a3 2) (3x)2 9x2

Simplify (4r)3 12r3 12r4 64r3 64r4

This is a combination of all of the other rules. Power of a Monomial This is a combination of all of the other rules. 1) (x3y2)4 x3• 4 y2• 4 x12 y8 2) (4x4y3)3 64x12y9

Simplify (3a2b3)4 12a8b12 81a6b7 81a16b81 81a8b12