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

You try: 53 · 56 59 24 · 2 -3 21

Multiplication Properties of Exponents ALGEBRA 1 LESSON 8-3 Simplify each expression. a. p2 • p • p5 Add exponents of powers with the same base. p 2 + 1 + 5 = = p 8 Simplify. 4x6 • 5x–4 b. Commutative Property of Multiplication (4 • 5)(x 6 • x –4) = Add exponents of powers with the same base. = 20(x 6+(–4)) Simplify. = 20x 2 8-3

You try: n2 · n3 · 7n 7n6

Multiplication Properties of Exponents ALGEBRA 1 LESSON 8-3 Simplify each expression. a. a 2 • b –4 • a 5 Commutative Property of Multiplication a 2 • a 5 • b –4 = = a 2 + 5 • b –4 Add exponents of powers with the same base. Simplify. a 7 b 4 = Commutative and Associative Properties of Multiplication (2 • 3 • 4)(p 3)(q • q 4) = b. 2q • 3p3 • 4q4 = 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. = 24p 3q 5 Simplify. 8-3

You try: 2y3 · 7x2 · 2y4 28 · x2 · y7

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) = Commutative and Associative Properties of Multiplication (3 • 7)(10–3 • 10–5) = 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. 8-3

You try: (1.5 · 10-2) ( 3 · 104) 4.5 · 102

Multiplication Properties of Exponents ALGEBRA 1 LESSON 8-3 pages 407–410  Exercises 1. 210 2. 3. 1 4. (0.99)3 5. 69 6. 1 7. c5 8. 3r 5 9. 10t –7 10. 56x 6 11. 3x4 22. 6  105 23. 6  109 24. 4  103 25. 3.4  10–5 26. 5.6  10–7 1.5  1022 2.55 x 1013 1.08 x 1021 3.84 x 105 9 -4 -3 12. –4.8n3 13. b3 14. –7 15. –45a4 16. 17. 45x 7y 6 18. 12a6c8 19. x10y2 20. a8b 21. – 25 58 y3 x 240m3 r 8-3

Multiplication Properties of Exponents ALGEBRA 1 LESSON 8-3 Simplify each expression. 1. 34 • 35 2. 4x5 • 3x–2 3. (3  104)(5  102) 4. (7  10–4)(1.5  105) 5. (–2w –2)(–3w2b–2)(–5b–3) 6. What is 2 trillion times 3 billion written in scientific notation? 39 12x3 1.5  107 1.05  102 30 b5 – 6  1021 8-3