More Multiplication Properties of Exponents Rewrite each expression

More Multiplication Properties of Exponents Rewrite each expression using each base only once. ALGEBRA 1 LESSON 8 -4 (For help, go to Lesson 8 -3. ) 1. 32 • 32 2. 23 • 23 3. 57 • 57 4. 7 • 7 Simplify. 5. x 3 • x 3 6. a 2 • a 2 7. y– 2 • y– 2 8. n– 3 • n– 3 4 -4

More Multiplication Properties of Exponents Solutions ALGEBRA 1 LESSON 8 -4 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 7. y– 2 • y– 2 = y(– 2 + (– 2)) = y– 6 = y 6 8. n– 3 • n– 3 = n(– 3 + (– 3)) = n– 6 = 1 6 n 4 -4

More Multiplication Properties of Exponents ALGEBRA 1 LESSON 8 -4 Simplify (a 3)4 = a 3 • 4 = a 12 Multiply exponents when raising a power to a power. Simplify. 4 -4

More Multiplication Properties of Exponents ALGEBRA 1 LESSON 8 -4 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– 4 Simplify. 1 = b 4 Write using only positive exponents. 4 -4

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

More Multiplication Properties of Exponents ALGEBRA 1 LESSON 8 -4 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– 7 • y 6 Add exponents of powers with the same base. 16 y 6 = x 7 Simplify. 4 -4

More Multiplication Properties of Exponents ALGEBRA 1 LESSON 8 -4 An object has a mass of 102 kg. The expression 102 • (3 108)2 describes the amount of resting energy in joules the object contains. Simplify the expression. 102 • (3 108)2 = 102 • 32 • (108)2 Raise each factor within parentheses to the second power. = 102 • 32 • 1016 Simplify (108)2. = 32 • 1016 Use the Commutative Property of Multiplication. = 32 • 102 + 16 Add exponents of powers with the same base. = 9 1018 Simplify. Write in scientific notation. 4 -4

More Multiplication Properties of Exponents Simplify each expression. ALGEBRA 1 LESSON 8 -4 1. (x 4)5 3. (5 x 4)3 x 20 2. 125 x 12 4. (1. 5 105)2 5. (2 w– 2)4(3 w 2 b– 2)3 432 b 6 w 2 x(x 5 y– 2)3 x 16 y 6 2. 25 1010 6. (3 10– 5)(4 104)2 4 -4 4. 8 103