1. ALGEBRA 1 Lesson 7-3 Warm-Up

2. ALGEBRA 1 “Multiplication Properties of Exponents” (7-3) 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

3. ALGEBRA 1 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) = Multiplication Properties of Exponents LESSON 7-3 Additional Examples

4. ALGEBRA 1 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 ) Multiplication Properties of Exponents LESSON 7-3 Additional Examples

5. ALGEBRA 1 “Multiplication Properties of Exponents” (7-3) How do you multiply numbers in scientific notation? When you multiply numbers in scientific notation, multiply the decimal numbers together and add the exponents together. Example:

6. ALGEBRA 1 Simplify (3  10 –3 )(7  10 –5 ). Write the answer in scientific notation. = 21  10 –8 Simplify. = (2.1  10 1 ) 10 –8 Write 21 in scientific notation. = 2.1  10 1 + (– 8) Add exponents of powers with the same base. = 2.1  10 –7 Simplify. (3  10 –3 )(7  10 –5 ) = Commutative and Associative Properties of Multiplication (3 7)(10 –3 10 –5 ) Multiplication Properties of Exponents LESSON 7-3 Additional Examples

7. ALGEBRA 1 The speed of light is 3  10 8 m/s. If there are 1  10 –3 km in 1 m, and 3.6  10 3 s in 1 h, approximate the speed of light in km/h. Speed of light = meters seconds kilometers meters seconds hour Use dimensional analysis. = (3  10 8 ) (1  10 –3 ) (3.6  10 3 ) msms km m shsh Substitute. = (3 1 3.6)  (10 8 10 –3 10 3 ) Commutative and Associative Properties of Multiplication = 10.8  (10 8 + (– 3) + 3 ) Simplify. Multiplication Properties of Exponents LESSON 7-3 Additional Examples

8. ALGEBRA 1 = 10.8  10 8 Add exponents. = (1.08  10 1 ) 10 8 Write 10.8 in scientific notation. = 1.08  10 9 Add the exponents. The speed of light is about 1.08  10 9 km/h. (continued) Multiplication Properties of Exponents LESSON 7-3 Additional Examples

9. ALGEBRA 1 Simplify each expression. 1.3 4 3 5 2.4x 5 3x –2 3.(–2w –2 )(–3w 2 b –2 )(–5b –3 ) Write each product using scientific notation. 4. (3  10 4 )(5  10 2 )5.(7  10 –4 )(1.5  10 5 ) 6. What is 2 trillion times 3 billion written in scientific notation? 3939 12x 3 1.5  10 7 1.05  10 2 30 b 5 – 6  10 21 Multiplication Properties of Exponents LESSON 7-3 Lesson Quiz