8 3 Multiplying Monomials Objective To multiply powers

8 -3 Multiplying Monomials Objective: To multiply powers.

POWER RULES When multiplying in the same base, multiply coefficients & add exponents. Rule 1: am(an)= am+n Ex. ) x 2(x 5) = x 7 Ex. ) (3 m 2)(2 m 4) (3)(2)(m 2+4)= 6 m 6

Multiplication Properties of Exponents Rewrite each expression using each base only once. a. 73 • 72 = 73 + 2 = 75 b. 44 • 41 • 4– 2 = 44 + 1 – 2 = 43 Add exponents of powers with the same base. Simplify the sum of the exponents. Think of 4 + 1 – 2 as 4 + 1 + (– 2) to add the exponents. Simplify the sum of the exponents. = 60 Add exponents of powers with the same base. Simplify the sum of the exponents. =1 Use the definition of zero as an exponent. c. 68 • 6– 8 = 68 + (– 8) 8 -3

Example 1, page 405 A) 53 • 56 C) 7 -3 • 72 • 76 B) 24 • 2 -3

Multiplication Properties of Exponents Simplify each expression. a. p 2 • p 5 = p 2 + 1 + 5 = p 8 Add exponents of powers with the same base. Simplify. b. 4 x 6 • 5 x– 4 = (4 • 5)(x 6 • x – 4) Commutative Property of Multiplication = 20(x 6+(– 4)) Add exponents of powers with the same base. = 20 x 2 Simplify. 8 -3

Example 2, page 406 A) a • a 5 C) 6 y 2 • 3 y 3 • 2 y-4 b) n 2 • n 3 • 7 n

Multiplication Properties of Exponents Simplify each expression. a. a 2 • b – 4 • a 5 = a 2 • a 5 • b – 4 Commutative Property of Multiplication Add exponents of powers with the same base. = a 2 + 5 • b – 4 a 7 = 4 b b. Simplify. 2 q • 3 p 3 • 4 q 4 = (2 • 3 • 4)(p 3)(q • q 4) Commutative and Associative Properties of Multiplication = 24(p 3)(q 1 • q 4) Multiply the coefficients. Write q as q 1. = 24(p 3)(q 1 + 4) Add exponents of powers with the same base. = 24 p 3 q 5 Simplify. 8 -3

Example 3, page 406 A) a • b • a 5 C) m 2 • n-2 • 7 m B) 2 y 3 • 7 x 2 • 2 y 4

Here’s some more. Ex. ) (21 c 6)(c 7) Ex. ) (8 x 4)(3 x) Ex. ) (2 a 4)(2 a 3 b 2)(-3 ab 3)

Summary What did you learn today?

Summary Rule 1: am(an)= am+n

ASSIGNMENT #8 -3, page 407, 1 -21, odd 31 -47, odd 79 -99