1. Preview
Warm Up
California Standards
Lesson Presentation

2. Warm Up
Write in exponential form.
1. 6 · 6 · 6 · 6 · 6
2. 3x · 3x · 3x · 3x
Simplify.
3. 34
4. (–3)5
5. (24)5
6. (42)0 65
(3x)4 81
–243
220 1

3. California
Standards
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

4. 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, , 2x
8 w3
To multiply two monomials, multiply the coefficients and add the exponents that have the same base.

5. Additional Example 1: Multiplying Monomials
A. (3a2)(4a5)
Use the Comm. and Assoc. Properties.
(3 ∙ 4)(a2 ∙ a5)
3 ∙ 4 ∙ a2 + 5
Multiply coefficients. Add
exponents that have the same base.
12a7
B. (4x2y3)(5xy5)
Use the Comm. and Assoc. Properties. Think: x = x1.
(4 ∙ 5)(x2 ∙ x)(y3 ∙ y5)
(4 ∙ 5)(x2 ∙ x1)(y3 ∙ y5)
Multiply coefficients. Add
exponents that have the same base.
4 ∙ 5 ∙ x2 + 1 ∙ y3+5
20x3y8

6. Additional Example 1: Multiplying Monomials
C. (–3p2r)(6pr3s)
Use the Comm. and Assoc. Properties.
(–3 ∙ 6)(p2 ∙ p)(r ∙ r3)(s)
(–3 ∙ 6)(p2 ∙ p1)(r1 ∙ r3)(s)
Multiply coefficients. Add
exponents that have the same base.
–3 ∙ 6 ∙ p2 + 1 ∙ r1+3 ∙ s
–18p3r4s

7. Check It Out! Example 1
Multiply.
A. (2b2)(7b4)
Use the Comm. and Assoc. Properties.
(2 ∙ 7)(b2 ∙ b4)
2 ∙ 7 ∙ b2 + 4
Multiply coefficients. Add
exponents that have the same base.
14b6
B. (4n4)(5n3)(p)
Use the Comm. and Assoc. Properties.
(4 ∙ 5)(n4 ∙ n3)(p)
Multiply coefficients. Add
exponents that have the same base.
4 ∙ 5 ∙ n4 + 3 ∙ p
20n7p

8. Check It Out! Example 1
Multiply.
C. (–2a4b4)(3ab3c)
Use the Comm. and Assoc. Properties.
(–2 ∙ 3)(a4 ∙ a)(b4 ∙ b3)(c)
(–2 ∙ 3)(a4 ∙ a1)(b4 ∙ b3)(c)
Multiply coefficients. Add
exponents that have the same base.
–2 ∙ 3 ∙ a4 + 1 ∙ b4+3 ∙ c
–6a5b7c

9. To divide a monomial by a monomial, divide the coefficients and subtract the exponents of the powers in the denominator from the exponents of the powers in the numerator that have the same base.

10. Additional Example 2: Dividing Monomials
Divide. Assume that no denominator equals zero.
15m5 3m2 A.
m5-2
15 3
Divide coefficients. Subtract
exponents that have the same base.
5m3
18a2b3 16ab3 B.
a2-1 b3-3
9 8
Divide coefficients. Subtract
exponents that have the same base. a
9 8

11. Check It Out! Example 2
Divide. Assume that no denominator equals zero.
18x7 6x2 A.
x7-2
18 6
Divide coefficients. Subtract
exponents that have the same base.
3x5
12m2n3 9mn2 B.
m2-1 n3-2
4 3
Divide coefficients. Subtract
exponents that have the same base. mn
4 3

12. 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

13. Additional Example 3: Raising a Monomial to a Power
Simplify.
A. (3y)3
33 ∙ y3
Raise each factor to the power.
27y3
B. (2a2b6)4
24 ∙ (a2)4 ∙ (b6)4
Raise each factor to the power.
16a8b24
Multiply exponents.

14. Check It Out! Example 3
Simplify.
A. (4a)4
44 ∙ a4
Raise each factor to the power.
256a4
B. (–3x2y)2
(–3)2 ∙ (x2)2 ∙ (y)2
Raise each factor to the power.
9x4y2
Multiply exponents.

15. Lesson Quiz
Multiply.
1. (3g2h3)(–6g7h2) 2. (12m3)(3mp3)
Divide. Assume that no denominator equals zero.
–18g9h5
36m4p3
6a6b4 3a2b
9x3y 6x2y
3 2 x
20p5q –4p2q
2a4b3
–5p3
Simplify.
6.(–5y7)3
7. (3c2d3)4
8. (3m2n)5
–125y21
81c8d12
243m10n5