1. Write in exponential form. 1. 6 · 6 · 6 · 6 · 6 2. 3x · 3x · 3x · 3x Simplify. 3. 3 4 4. (–3) 5 5. (2 4 ) 5 6. (4 2 ) 0 6565 (3x) 4 81 –243 2 20 1 Warm Up

2. Multiplying and Dividing Monomials Section 4.4

3. AF2.2 Multiply and divide monomials; extend the process of taking powers and extracting roots to monomials when the latter results in a monomial with an integer exponent. Also covered: AF1.3 California Standards

4. Words to Know A monomial is a number or a product of numbers and variables with exponents that are whole numbers. Monomials Not monomials 7x 5,  3a 2 b 3, n 2, 8, z4z4 m  3,4z 2.5, 5 + y,, 2 x 8w38w3

5. Multiplying Monomials 1. Multiply just the coefficients first. 2. Add the exponents that have the same base.

6. Multiplying Monomials 1. (4x 2 y 3 )(5xy 5 ) 20x 3 y 8 2. (–3p 2 r)(6pr 3 s) –18p 3 r 4 s 1. Multiply just the coefficients first. 2. Add the exponents that have the same base.

7. Try on your own….. Multiply. A. (2b 2 )(7b 4 ) 14b 6 B. (4n 4 )(5n 3 )(p) 20n 7 p C. (–2a 4 b 4 )(3ab 3 c) –6a 5 b 7 c

8. Dividing Monomials 15m 5 3m 2 1. Divide just the coefficients first. 2. Subtract the exponents that have the same base.

9. Dividing Monomials 18a 2 b 3 16ab 3 a 9898 18x 7 6x 2 3x53x5 12m 2 n 3 9mn 2 mn 4343

10. Raising a monomial to a power… To raise a monomial to a power, you must first understand how to find a power of a product. Notice what happens to the exponents when you find a power of a product. (xy) 3 = xy ∙ xy ∙ xy = x ∙ x ∙ x ∙ y ∙ y ∙ y = x 3 y 3

11. Raising a monomial to a power… Simplify. A. (3y) 3 27y 3 B. (2a 2 b 6 ) 4 16a 8 b 24 3 3 ∙ y 3 2 4 ∙ (a 2 ) 4 ∙ (b 6 ) 4

12. Try on your own…. A. (4a) 4 256a 4 B. (–3x 2 y) 2 9x4y29x4y2

13. Summary When multiplying a monomial, remember to add the exponents. When dividing monomials, remember to subtract the exponents.

14. Lesson Quiz Multiply. 1. (3g 2 h 3 )(–6g 7 h 2 ) 2. (12m 3 )(3mp 3 ) Divide. Assume that no denominator equals zero. 3. 4. 5. 36m 4 p 3 –18g 9 h 5 2a4b32a4b3 3 2 x –5p 3 Simplify. 6.(–5y 7 ) 3 7. (3c 2 d 3 ) 4 8. (3m 2 n) 5 81c 8 d 12 –125y 21 243m 10 n 5 6a6b43a2b6a6b43a2b 9x3y6x2y9x3y6x2y 20p 5 q –4p 2 q