1. PRE-ALGEBRA

2. Lesson 4-7 Warm-Up

3. PRE-ALGEBRA How do you multiply numbers with the same base? How do you multiply powers in algebraic expressions? Rule: When you multiply exponents with the same nonzero base (a ≠ 0), add the exponents. Example: 2 3  2 4 = (2 · 2 · 2)  (2 · 2 · 2 · 2) = 2 7 Example: -2x · 3x 5 = -2 · 3 · x 1 · x 5 = -6x 6 To multiply power in algebraic expressions, multiply the coefficients together and add the exponents of like terms (same variables) together. Example: a m · a n = a m+n Exponents and Multiplication (4-7)

4. PRE-ALGEBRA Write the expression using a single exponent. (–3) 2 (–3) 4 = (–3) (6) Simplify the exponent. Add the exponents. = (–3) (2+4) (–3) 4 (–3) 2 Additional Examples Exponents and Multiplication LESSON 4-7

5. PRE-ALGEBRA Rewrite each expression using each base only once. 7 3 7 2 = 7 5 Simplify the sum of the exponents. 4 4 4 1 4 –2 = 4 3 Simplify the sum of the exponents. = 6 0 Simplify the sum of the exponents. Use the definition of zero as an exponent.= 1 a. b. 6 8 6 –8 c. Add exponents of powers with the same base. 7 3 + 2 = Think of 4 + 1 – 2 as 4 + 1 + (–2) to add the exponents. 4 4 + 1 – 2 = Add exponents of powers with the same base. 6 8 + (–8) = Additional Examples Exponents and Multiplication LESSON 4-7

6. PRE-ALGEBRA Simplify each expression. p 2 p p 5 a. = p 8 Simplify. Multiply the coefficients. Write q as q 1. = 24(p 3 ) (q 1 q 4 ) Simplify. = 24p 3 q 5 2q 3p 3 4q 4 b. Commutative and Associative Properties of Multiplication (2 3 4)(p 3 )(q q 4 ) = Add exponents of powers with the same base. p 2 + 1 + 5 = Add exponents of powers with the same base. = 24(p 3 ) (q 1 + 4 ) Additional Examples Exponents and Multiplication LESSON 4-7

7. PRE-ALGEBRA Simplify 3a 3 (–5a 4 ). 3a 3 (–5a 4 ) = 3 (–5) a 3 a 4 Use the Commutative Property of Multiplication. Add the exponents.= –15a 3 + 4 Simplify.= –15a 7 Exponents and Multiplication LESSON 4-7 Additional Examples

8. PRE-ALGEBRA “Power Rules” (10-2) What happens when you raise a power to a power? Rule: When you raise a power to a power [Example: (a m ) n ], multiply the powers together. Example: (7 2 ) 3 = (7 2 ) · (7 2 ) · (7 2 ) = (7 · 7) · (7 · 7) · (7 · 7) = 7 6 Example: (a 6 ) 2 = a 6 · a 6 = (a · a · a · a · a · a) · (a · a · a · a · a · a) = a 12 (a m ) n · a mn

9. PRE-ALGEBRA Write the expression using a single exponent. a. (5 –2 ) 3 b. (8 –4 ) –5 Multiply the exponents. = 5 (–2 3) = 8 (–4 –5) Simplify the exponent. = 5 –6 = 8 20 = 156156 Write with a positive exponent. LESSON 4-7 Additional Examples Exponents and Multiplication

10. PRE-ALGEBRA Simplify each expression. a. (2 3 ) 3 = (2) 9 Simplify the exponent. (2 3 ) 3 = (2) 3 3 Multiply the exponents. = 512Simplify. b. (g 5 ) 4 (g 5 ) 4 = g 5 4 Multiply the exponents. = g 20 Simplify the exponent. Exponents and Multiplication LESSON 4-7 Additional Examples

11. PRE-ALGEBRA Simplify each expression. 1.(0.2) 2 (0.2) 3 2.g 2 h 2 h 4 h 3.4r s 7r s 5 4.–(2 2 ) 5 5.(v 3 ) 8 0.00032 g 2 h 7 –1,024 v 24 6 3 28r s 6 9 Lesson Quiz Exponents and Multiplication LESSON 4-7