2. Lesson Menu Main Idea and New Vocabulary Key Concept:Product of Powers Example 1:Multiply Powers Example 2:Multiply Monomials Example 3:Multiply Monomials Key Concept:Quotient of Powers Example 4:Divide Powers Example 5:Divide Powers Example 6:Real-World Example

3. Main Idea/Vocabulary Multiply and divide monomials. monomial

4. Key Concept

5. Example 1 Multiply Powers Find 8 5 8. Express using exponents. 8 5 8= 8 5  8 1 8 = 8 1 = 8 5 + 1 The common base is 8. = 8 6 Add the exponents. Answer: 8 6 Check 8 5 8= (8 8 8 8 8) 8 = 8 8 8 8 8 8 or 8 6

6. Example 1 CYP A.4 2 B.4 4 C.4 6 D.4 8 Find 4 4 4 2. Express using exponents.

7. Example 2 Find f 6 f 3. Multiply Monomials f 6 f 3 = f 6 + 3 The common base is f. = f 9 Add the exponents. Answer: f 9

8. Example 2 CYP A.g 7 B.g 11 C.g 18 D.g 29 Find g 2 g 9.

9. Example 3 Multiply Monomials Find –3x 6 y 2 2x 4 y 3. (–3x 6 y 2 )(2x 4 y 3 ) = (–3  2)(x 6  x 4 ) (y 2  y 3 ) Use the Commutative and Associative Properties. = (–6)(x 6 + 4 ) (y 2 + 3 ) The common bases are x and y. = –6x 10 y 5 Add the exponents. Answer: –6x 10 y 5

10. Example 3 CYP A.4x 7 y B.–4x 7 y C.4xy D.–4xy Find –1x 3 –4x 4 y.

11. Key Concept 4

12. Example 4 Find Divide Powers = 4 7 Subtract the exponents. Answer: 4 7 The common base is 4.

13. Example 4 CYP A.3 15 B.3 8 C.3 2 D.3 Find

14. Example 5 Divide Powers Find. = x 2 Subtract the exponents. Answer: x 2 The common base is x.

15. Example 5 CYP A.y B.y 8 C.y 15 D.y 56 Find

16. Example 6 BACTERIA A scientist determines that Bacteria A multiply at a rate of 9 8 per second. Bacteria B were determined to multiply at a rate of 9 5 per second. Find how many times faster Bacteria A multiply than Bacteria B. = 9 3 Subtract the exponents. Answer:So, Bacteria A multiply 9 3 or 729 times faster than Bacteria B. The common base is 9.

17. Example 6 CYP A.2 times more B.3 times more C.2 2 times more D.2 4 times more PICTURES Alexi took 2 5 pictures on the class trip. Brittany took 2 4 pictures. Find how many more pictures Alexi took than Brittany.