Multiplication Properties of Exponents Rewrite each expression using

Multiplication Properties of Exponents Rewrite each expression using exponents. ALGEBRA 1 LESSON 8 -3 (For help, go to Lesson 1 -6. ) 1. t • t • t • t 2. (6 – m)(6 – m) 3. (r + 5)(r + 5) 4. 5 • 5 • s • s Simplify. 5. – 54 6. (– 5)4 7. (– 5)0 8. (– 5)– 4 4 -3

Multiplication Properties of Exponents Solutions ALGEBRA 1 LESSON 8 -3 1. t • t • t • t = t 7 2. (6 – m)(6 – m) = (6 – m)3 3. (r + 5)(r + 5) = (r + 5)5 4. 5. 6. 7. 8. 5 • 5 • s • s = 53 • s 3 = 53 s 3 – 54 = –(5 • 5 • 5) = –(25 • 25) = – 625 (– 5)4 = (– 5)(– 5) = (25) = 625 (– 5)0 = 1 (– 5)– 4 = (– 1 )4 5 = (– 1 )(– 1 ) 5 5 = ( 1 ) 25 25 1 = 625 5 5 4 -3

Multiplication Properties of Exponents ALGEBRA 1 LESSON 8 -3 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) 4 -3

Multiplication Properties of Exponents ALGEBRA 1 LESSON 8 -3 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. 4 -3

Multiplication Properties of Exponents ALGEBRA 1 LESSON 8 -3 Simplify each expression. 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. 4 -3

Multiplication Properties of Exponents ALGEBRA 1 LESSON 8 -3 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 Add exponents of powers with the same base. 101 + (– 8) = 2. 1 10– 7 Simplify. 4 -3

Multiplication Properties of Exponents ALGEBRA 1 LESSON 8 -3 The speed of light is 3 108 m/s. If there are 1 10– 3 km in 1 m, and 3. 6 103 s in 1 h, find the speed of light in km/h. Speed of light = meters kilometers seconds • • seconds meters hour m km s = (3 108) s • (1 10– 3) • (3. 6 103) m h = (3 • 1 • 3. 6) (108 • 10– 3 • 103) = 10. 8 (108 + (– 3) + 3) Use dimensional analysis. Substitute. Commutative and Associative Properties of Multiplication Simplify. 4 -3

Multiplication Properties of Exponents ALGEBRA 1 LESSON 8 -3 (continued) = 10. 8 108 Add exponents. = 1. 08 101 • 108 Write 10. 8 in scientific notation. = 1. 08 109 Add the exponents. The speed of light is about 1. 08 109 km/h. 4 -3

Multiplication Properties of Exponents Simplify each expression. ALGEBRA 1 LESSON 8 -3 1. 34 • 35 39 2. 4 x 5 • 3 x– 2 7 3. (3 104)(5 102) 1. 5 10 5. (– 2 w – 2)(– 3 w 2 b– 2)(– 5 b– 3) – 12 x 3 2 4. (7 10– 4)(1. 5 105) 1. 05 10 30 b 5 6. What is 2 trillion times 3 billion written in scientific notation? 6 1021 4 -3