1. Multiplying and Dividing Monomials

2. Objectives: Understand the concept of a monomial
Use properties of exponents to simplify expressions

3. Monomial An expression that is either: a constant a variable
5, -21, 0
a variable
a product of a constant and 1 or
more variables
2x, 4ab2, -7m3n8

4. Multiply (a3b4)(a5b2) (a3a5)(b4b2) Answer: a8b6 Group like bases
Which property was applied?
Commutative Property
Answer: a8b6
When multiplying, add the exponents.

5. Multiply
(5a4b3)(2a6b5)

6. Multiply
(5a4b3)(2a6b5)
Multiply the coefficients

7. Multiply (5a4b3)(2a6b5) 10(a4b3)(a6b5) 10(a4a6)(b3b5) Answer: 10 a10b8
Multiply the coefficients
Group like bases
10(a4a6)(b3b5)
Answer: 10 a10b8
When multiplying, add the exponents.

8. Try This! 1. (a2b3)(a9b) 2. (3a12b4)(-5ab2)(a3b8) Answer: a11b4

9. Divide a7b5 a4b a7 b5 a4 b1 (a7 - 4)(b5 - 1) Answer: a3b4•
Group like bases
When dividing,
subtract the exponents
(a7 - 4)(b5 - 1)
Answer: a3b4

10. Divide -30x3y4 -5xy3 -30 -5 (x3 - 1)(y4 - 3) Answer: 6x2y
Divide the coefficients.
Group like bases
(x3 - 1)(y4 - 3)
Answer: 6x2y

11. Divide 2m5n4 -3m4n2 2 -3 (m5 - 4)(n4 - 2) - 3 - 3 mn2 2mn2 Answer: 2
Divide the coefficients.
Group like bases
(m5 - 4)(n4 - 2)
2mn2
- 3 =
Answer: 2
- 3
mn2

12. Try This! 1. m8n5 m4n2 2. - 3x10y7 6x9y2 - 3 6 (m8 - 4)(n5 - 2)=
Answer: -1 2
xy5
Answer: m4n3

13. Power of a Product (ab)3 (ab)2 (ab)(ab)(ab) (ab)(ab) (aaa)(bbb)
Rule 4: (xy)n = xnyn
Multipy the exponent outside the () times each
exponent inside the ().

14. Power of a Product (4m11n20)2 (a9b5)3 (41m11n20)2 (a9•3)(b5•3)
Answer: a27b15
Answer: 16m22n40
Rule 4: (xy)n = xnyn

15. 4 x y x y • = x4 y4
Rule 5: x y n = xn yn

16. Try This! 2. (4xy5z2)4 1. (2a4)3 (41x1y5z2)4 (21a4)3 (21•3)(a4•3)
Answer: 8a12
Answer: 256x4y20z8
Rule 4: (xy)n = xnyn