1. Holt Algebra 1 7-4 Division Properties of Exponents 7-4 Division Properties of Exponents Holt Algebra 1 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation

2. Holt Algebra 1 7-4 Division Properties of Exponents Warm Up Simplify. 1. (x 2 ) 3 3. 5. 2.2. 4. 6.

3. Holt Algebra 1 7-4 Division Properties of Exponents Use division properties of exponents to evaluate and simplify expressions. Objective

4. Holt Algebra 1 7-4 Division Properties of Exponents A quotient of powers with the same base can be found by writing the powers in a factored form and dividing out common factors. Notice the relationship between the exponents in the original quotient and the exponent in the final answer: 5 – 3 = 2.

5. Holt Algebra 1 7-4 Division Properties of Exponents

6. Holt Algebra 1 7-4 Division Properties of Exponents Simplify. Example 1: Finding Quotients of Powers A.B.

7. Holt Algebra 1 7-4 Division Properties of Exponents C. Simplify. Example 1: Finding Quotients of Powers D.

8. Holt Algebra 1 7-4 Division Properties of Exponents Both and 729 are considered to be simplified. Helpful Hint

9. Holt Algebra 1 7-4 Division Properties of Exponents Check It Out! Example 1 a. Simplify. b.

10. Holt Algebra 1 7-4 Division Properties of Exponents Check It Out! Example 1 Simplify. c.d.

11. Holt Algebra 1 7-4 Division Properties of Exponents A power of a quotient can be found by first writing the numerator and denominator as powers. Notice that the exponents in the final answer are the same as the exponent in the original expression.

12. Holt Algebra 1 7-4 Division Properties of Exponents

13. Holt Algebra 1 7-4 Division Properties of Exponents Simplify. Example 4A: Finding Positive Powers of Quotient Use the Power of a Quotient Property. Simplify.

14. Holt Algebra 1 7-4 Division Properties of Exponents Simplify. Example 4B: Finding Positive Powers of Quotient Use the Power of a Product Property. Use the Power of a Product Property: Simplify and use the Power of a Power Property:

15. Holt Algebra 1 7-4 Division Properties of Exponents Simplify. Example 4C: Finding Positive Powers of Quotient Use the Power of a Product Property. Use the Power of a Product Property:

16. Holt Algebra 1 7-4 Division Properties of Exponents Simplify. Example 4C Continued Use the Power of a Product Property:

17. Holt Algebra 1 7-4 Division Properties of Exponents Check It Out! Example 4a Simplify. Use the Power of a Quotient Property. Simplify.

18. Holt Algebra 1 7-4 Division Properties of Exponents Check It Out! Example 4b Simplify.

19. Holt Algebra 1 7-4 Division Properties of Exponents Check It Out! Example 4c Simplify.

20. Holt Algebra 1 7-4 Division Properties of Exponents Therefore, Write the fraction as division. Use the Power of a Quotient Property. Multiply by the reciprocal. Simplify. Use the Power of a Quotient Property. Remember that What if x is a fraction?.

21. Holt Algebra 1 7-4 Division Properties of Exponents

22. Holt Algebra 1 7-4 Division Properties of Exponents Simplify. Example 5A: Finding Negative Powers of Quotients Rewrite with a positive exponent. and Use the Powers of a Quotient Property.

23. Holt Algebra 1 7-4 Division Properties of Exponents Simplify. Example 5B: Finding Negative Powers of Quotients

24. Holt Algebra 1 7-4 Division Properties of Exponents Simplify. Example 5C: Finding Negative Powers of Quotients Rewrite each fraction with a positive exponent. Use the Power of a Quotient Property. Use the Power of a Product Property: (3) 2  (2n) 3 = 3 2  2 3 n 3 and (2) 2  (6m) 3 = 2 2  6 3 m 3

25. Holt Algebra 1 7-4 Division Properties of Exponents 1 24 1 2 1 12 Divide out common factors. Simplify. Example 5C: Finding Negative Powers of Quotients Simplify. Square and cube terms.

26. Holt Algebra 1 7-4 Division Properties of Exponents Whenever all of the factors in the numerator or the denominator divide out, replace them with 1. Helpful Hint

27. Holt Algebra 1 7-4 Division Properties of Exponents Check It Out! Example 5a Simplify. 9 3 =729 and 4 3 = 64. Use the power of a Quotient Property. Rewrite with a positive exponent.

28. Holt Algebra 1 7-4 Division Properties of Exponents Check It Out! Example 5b Simplify. Rewrite with a positive exponent. Use the Power of a Power Property: (b 2 c 3 ) 4 = b 24 c 34 = b 8 c 12 and (2a) 4 = 2 4 a 4 = 16a 4. Use the Power of a Quotient Property.

29. Holt Algebra 1 7-4 Division Properties of Exponents Check It Out! Example 5c Simplify. Rewrite each fraction with a positive exponent. Use the Power of a Quotient Property. Use the Power of a Product Property: (3) 2 = 9. Add exponents and divide out common terms.

30. Holt Algebra 1 7-4 Division Properties of Exponents Lesson Quiz: Part I 1. 3. 4. 5. 2. Simplify.