Multiplication Properties of Exponents ALGEBRA 1 LESSON 1

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

Multiplication Properties of Exponents ALGEBRA 1 LESSON 1 -6 Solutions 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. 5 • 5 • s • s = 53 • s 3 = 53 s 3 – 54 = –(5 • 5 • 5) = –(25 • 25) = – 625 (– 5)4 = (– 5)(– 5) = (25) = 625 (– 5)1 = – 5 1 -6

Multiplication Properties of Exponents ALGEBRA 1 LESSON 1 -6 Rewrite each expression using each base only once. a. 73 • 72 = 73 + 2 = 75 b. 42 • 41 = 42 + 1 = 43 Add exponents of powers with the same base. Simplify the sum of the exponents. Think of 2 + 1 to add the exponents. Simplify the sum of the exponents. 1 -6

Multiplication Properties of Exponents ALGEBRA 1 LESSON 1 -6 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 10 Simplify. 1 -6

Multiplication Properties of Exponents ALGEBRA 1 LESSON 1 -6 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 = b. a 7 b 4 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. 1 -6

Multiplication Properties of Exponents ALGEBRA 1 LESSON 1 -6 Simplify each expression. 1. 34 • 35 39 6 3. (3 104)(5 102) 15 10 2. 4 x 5 • 3 x 2 12 x 7 4. (7 104)(15 105) 1 -6 105 109

More Multiplication Properties of Exponents ALGEBRA 1 LESSON 1 -6 (For help, go to Lesson 1 -6. ) Rewrite each expression using each base only once. 1. 32 • 32 2. 23 • 23 3. 57 • 57 4. 7 • 7 Simplify. 5. x 3 • x 3 6. a 2 • a 2 1 -6

More Multiplication Properties of Exponents ALGEBRA 1 LESSON 1 -6 Solutions 1. 32 • 32 = 3(2 + 2) = 36 2. 23 • 23 = 2(3 + 3 + 3) = 212 3. 57 • 57 = 5(7 + 7 + 7) = 528 4. 7 • 7 = 73 5. x 3 • x 3 = x(3 + 3) = x 6 6. a 2 • a 2 = a(2 + 2) = a 6 1 -6

More Multiplication Properties of Exponents ALGEBRA 1 LESSON 1 -6 Simplify (a 3)4 = a 3 • 4 = a 12 Multiply exponents when raising a power to a power. Simplify. 1 -6

More Multiplication Properties of Exponents ALGEBRA 1 LESSON 1 -6 Simplify b 2(b 3)2 = b 2 • b 3 • 2 Multiply exponents in (b 3)– 2. = b 2 • b 6 Simplify. = b 2 + 6 Add exponents when multiplying powers of the same base. = b 8 Simplify. 1 -6

More Multiplication Properties of Exponents ALGEBRA 1 LESSON 1 -6 Simplify (4 x 3)2 = 42(x 3)2 Raise each factor to the second power. = 42 x 6 Multiply exponents of a power raised to a power. = 16 x 6 Simplify. 1 -6

More Multiplication Properties of Exponents ALGEBRA 1 LESSON 1 -6 Simplify (4 xy 3)2(x 3)3 = 42 x 2(y 3)2 • (x 3)3 Raise three factors to the second power. = 42 • x 2 • y 6 • x 9 Multiply exponents of a power raised to a power. = 42 • x 9 • y 6 Use the Commutative Property of Multiplication. = 42 • x 11 • y 6 Add exponents of powers with the same base. 16 x 11 y 6 = Simplify. 1 -6

More Multiplication Properties of Exponents ALGEBRA 1 LESSON 1 -6 Simplify each expression. 1. (x 4)5 3. (5 x 4)3 x 20 2. 125 x 12 4. (15 105)2 1 -6 x(x 5 y 2)3 x 16 y 6 225 1010