7 3 Multiplication Properties of Exponents Hubarth Algebra

7 -3 Multiplication Properties of Exponents Hubarth Algebra

Ex 1 Multiplying Powers 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)

Ex 2 Multiplying Powers in an Algebraic Expression Simplify each expression. a. p 2 • p 5 = p 2+1+5 Add exponents of powers with the same base. = p 8 Simplify. b. 2 q • 3 p 3 • 4 q 4 = (2 • 3 • 4)(p 3)(q • q 4) = 24(p 3) (q 1 + 4) = 24 p 3 q 5 Commutative and Associative Properties of Multiplication Multiply the coefficients. Write q as q 1. Add exponents of powers with the same base. Simplify.

Ex 3 Multiplying Numbers in Scientific Notation Simplify (3 10– 3)(7 10– 5). Write the answer in scientific notation. (3 10– 3)(7 10– 5) = (3 • 7)(10– 3 • 10– 5) Commutative and Associative Properties of Multiplication = 21 10– 8 Simplify. = 2. 1 101 • 10– 8 Write 21 in scientific notation. = 2. 1 101 + (– 8) Add exponents of powers with the same base. = 2. 1 10– 7 Simplify.

Practice