Write in exponential form.1. 6 · 6 · 6 · 6 · 62. 3x · 3x · 3x · 3xSimplify.3. 34 4. (–3)5

5. (24)5

6. (42)0

65

(3x)4

81–243220

1

Warm Up

Multiplying and Dividing Monomials

Section 4.4

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

Words to Know

A monomial is a number or a product of numbers and variables with exponents that are whole numbers.

Monomials

Not monomials

7x5, -3a2b3, n2, 8, z 4

m-3,4z2.5, 5 + y, , 2x8 w3

Multiplying Monomials

52 43 aa1. Multiply just the coefficients first.

2. Add the exponents that have the same base.

12 a 2 + 5

12a 7 It’s that easy!!

Multiplying Monomials

1. (4x2y3)(5xy5) 20x3y8

2. (–3p2r)(6pr3s) –18p3r4s

1. Multiply just the coefficients first.

2. Add the exponents that have the same base.

Try on your own…..Multiply.

A. (2b2)(7b4) 14b6

B. (4n4)(5n3)(p) 20n7p

C. (–2a4b4)(3ab3c) –6a5b7c

Dividing Monomials

15m5 3m2

1. Divide just the coefficients first.

2. Subtract the exponents that have the same base.

5 m 5 - 2

= 5m 3Great work!

Dividing Monomials

18a2b3 16ab3

a9 8

18x7 6x2

3x5

1.

2.

12m2n3 9mn2

mn4 3 3.

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 = x3y3

Raising a monomial to a power…

Simplify.

A. (3y)3 27y3

B. (2a2b6)4 16a8b24

33 ∙ y3

24 ∙ (a2)4 ∙ (b6)4

Try on your own….A. (4a)4 256a4

B. (–3x2y)2 9x4y2

SummaryWhen multiplying a monomial, remember to

add the exponents.

When dividing monomials, remember to subtract the exponents.

Lesson QuizMultiply.

1. (3g2h3)(–6g7h2) 2. (12m3)(3mp3)

Divide. Assume that no denominator equals zero.

3. 4. 5.

36m4p3–18g9h5

2a4b3 3 2 x –5p3

Simplify.

6.(–5y7)3

7. (3c2d3)4

8. (3m2n)5

81c8d12

–125y21

243m10n5

6a6b4 3a2b

9x3y 6x2y

20p5q –4p2q