1. ALGEBRA 1 Lesson 7-5 Warm-Up

2. ALGEBRA 1 “Division Properties of Exponents” (7-5) How do you divide powers with the same base? Rule: When you divide numbers with the same base, subtract the exponents. Example: = a 2 a m = a m - n b n 1 1 a 4 = a · a · a · a a 2 = a · a 1 1

3. ALGEBRA 1 Simplify each expression. x4x9x4x9 a. Simplify the exponents.= x –5 Rewrite using positive exponents. 1x5 1x5 = p 3 j –4 p –3 j 6 = p 6 j –10 Simplify. Rewrite using positive exponents. p 6 j 10 = b. = Subtract exponents when dividing powers with the same base. x 4 – 9 = Subtract exponents when dividing powers with the same base. p 3 – (–3) j –4 – 6 Division Properties of Exponents LESSON 7-5 Additional Examples

4. ALGEBRA 1 “Division Properties of Exponents” (7-5) How do you divide numbers in scientific notation form? Rule: When you divide numbers in scientific notation, divide the decimals and the exponents separately. Example: To find average, divide the number of tons by number of people

5. ALGEBRA 1 A small dog’s heart beats about 64 million beats in a year. If there are about 530 thousand minutes in a year, what is its average heart rate in beats per minute? 64 million beats 530 thousand min 6.4  10 7 beats 5.3  10 5 min =Write in scientific notation. 6.4 5.3  10 7–5 = Subtract exponents when dividing powers with the same base. 6.4 5.3  10 2 = Simplify the exponent. The dog’s average heart rate is about 121 beats per minute. Division Properties of Exponents LESSON 7-5 Additional Examples 121 Write in standard notation. 1.21  10 2 Divide. Round to the nearest hundredth.

6. ALGEBRA 1 ““Division Properties of Exponents” (7-5) What happens when you raise a quotient (like a / b) to a power? Rule: When you raise a quotient to a power [Example: (a / b) m, where a and b are nonzero numbers], raise the dividend and divisor (a and b) to the power separately.

7. ALGEBRA 1 Simplify. 3y 3 3y 3 4 3 4 y 12 =Multiply the exponent in the denominator. 81 y 12 = Simplify. 3 y 3 4 3434 (y 3)4(y 3)4 = Raise the numerator and the denominator to the fourth power. Division Properties of Exponents LESSON 7-5 Additional Examples

8. ALGEBRA 1 a. Simplify. 2323 –3 3 33233323 = Raise the numerator and the denominator to the third power. Simplify. 27 8 3 3838 or= 2323 –3 3232 3 = Rewrite using the reciprocal of. 2323 Division Properties of Exponents LESSON 7-5 Additional Examples

9. ALGEBRA 1 (continued) b. Simplify Raise the numerator and denominator to the second power. (–c) 2 (4b) 2 = Simplify. c 2 16b 2 = 4bc4bc – 4bc4bc – –2 c4b c4b – 2 = Rewrite using the reciprocal of. 4bc4bc – Write the fraction with a negative numerator. - c 4b 2 = –2. Division Properties of Exponents LESSON 7-5 Additional Examples

10. ALGEBRA 1 Simplify each expression. 1.2.3. 4.5.6. a 8 a –2 w3w7w3w7 (3a) 4 (2a –2 ) 6a 2 1.6  10 3 4  10 –2 245245 4x 33x 24x 33x 2 a 10 1 w 4 27 4  10 4 10 6 25 27 64x 3 2 –3 Division Properties of Exponents LESSON 7-5 Lesson Quiz