1. 3-2 Properties of Exponents Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 3-2 Properties of Exponents Warm Up Evaluate. 27 1. 3 3 2. 4 4 4 4 3. b 2 for b = 4 4. n 2 r for n = 3 and r = 2 256 16 18

3. 3-2 Properties of Exponents Learn to apply the properties of exponents.

4. 3-2 Properties of Exponents The factors of a power, such as 7 4, can be grouped in different ways. Notice the relationship of the exponents in each product. 7 7 7 7 = 7 4 (7 7 7) 7 = 7 3 7 1 = 7 4 (7 7) (7 7) = 7 2 7 2 = 7 4

5. 3-2 Properties of Exponents

6. 3-2 Properties of Exponents Example 1: Multiplying Powers with the Same Base A. 6 6 6 3 6 9 6 6 + 3 B. n 5 n 7 n 12 n 5 + 7 Add exponents. Multiply. Write the product as one power.

7. 3-2 Properties of Exponents D. 24 4 24 4 C. 2 5 2 2 6 2 5 + 1 24 8 4 + 4 Think: 2 = 2 1 Example 1: Multiplying Powers with the Same Base Continued Multiply. Write the product as one power. Add exponents.

8. 3-2 Properties of Exponents Check It Out E. 4 2 4 4 4 6 4 2 + 4 F. x 2 x 3 x 5 x 2 + 3 Add exponents. Multiply. Write the product as one power.

9. 3-2 Properties of Exponents H. 41 2 41 7 G. x 5 y 2 41 9 2 + 7 Check It Out Multiply. Write the product as one power. Cannot combine; the bases are not the same. Add exponents. x 5 y 2

10. 3-2 Properties of Exponents Notice what occurs when you divide powers with the same base. 5  5  55  5  5 5 5 5353 = 5  5  5  5  5 = 5  5 = 5 2 = 5  5  55  5  5 5  5  5  5  5

11. 3-2 Properties of Exponents Subtract exponents. 7 2 7 5 – 3 7 5 7 3 Example 2: Dividing Powers with the Same Base Divide. Write the quotient as one power. A. x 10 x 9 B. Subtract exponents. x 10 – 9 x Think: x = x 1

12. 3-2 Properties of Exponents Subtract exponents. 9797 9 9 – 2 9 9 9 2 Check It Out Divide. Write the product as one power. C. D. e 10 e 5 Subtract exponents. e 10 – 5 e 5

13. 3-2 Properties of Exponents Reading Math (9 ) is read as “nine to the fourth, to the fifth.” 5 4

14. 3-2 Properties of Exponents Simplify. Multiply exponents. Example 3: Raising a Power to a Power A. (5 4 ) 2 (5 4 ) 2 5 4 2 5858 B. (6 7 ) 9 (6 7 ) 9 6 7 9 6 63 Multiply exponents.

15. 3-2 Properties of Exponents Simplify. Multiply exponents. Example 3: Raising a Power to a Power C. D. (17 2 ) –20 (17 2 ) –20 17 2 –20 17 –40 Multiply exponents. 2323 12–3 2323 12 –3

16. 3-2 Properties of Exponents Simplify. Multiply exponents. Check It Out D. (3 3 ) 4 (3 3 ) 4 3 3 4 3 12 E. (4 8 ) 2 (4 8 ) 2 4 8 2 4 16 Multiply exponents.

17. 3-2 Properties of Exponents Simplify. Multiply exponents. Check It Out F. G. (13 4 ) –10 (13 4 ) –10 13 4 –10 13 –40 Multiply exponents. 1414 11–2 1414 11–2

18. 3-2 Properties of Exponents Lesson Quiz

19. 3-2 Properties of Exponents Lesson Quiz Write the product or quotient as one power. 3. 8 9 n 7 1. n 3  n 4 10 9 10 5 10 4 4. t 2 5. 3 2 3 3 3 5 3 10 2. 8 8 8 t 9 t 7 6. (m 2 ) 19 m 38 7. (9 -8 ) 9 9 –72 8. (10 4 ) 0 1