Lesson 8-1

Multiplying Monomials

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Objectives

• Multiply monomials

• Simplify expressions involving powers of monomials

Vocabulary

• Monomial – a number, a variable, or a product of a number and one or more variables A single term: 6, 2x, 14xy, -3x2y4 (includes products, but not quotients)

• Constant – a monomial that is a real number

Laws of Exponents

Multiplication: (add exponents)

b4 b6 = b4+6 = b10

Division: (subtract exponents)

b6 b4 = b6-4 = b2

Power Raised to a Power: (multiply exponents)

(b2)3 = b23 = b6

1 2 3 4 1 2 3 4 5 6 1 2 3 4 5 6 7 8 9 10

(bbbb) (bbbbbb) = bbbbbbbbbb

bbbbbb(bbbbbb) (bbbb) = ---------------------- = bb bbbb

1 2 1 2 1 2 1 2 3 4 5 6

(bb) (bb) (bb) = bbbbbb

Example 1

xyd.

c.

b.

a.

ReasonMonomial?Expression

Determine whether each expression is a monomial. Explain your reasoning.

The expression is the product of two variables.

yes

yes

The expression is the product of a number and two variables.

yes

The expression involves subtraction, not the product, of two variables.

no

is a real number and an

example of a constant.

Example 2a

Simplify .

Commutative and Associative Properties

Product of Powers

Simplify.Answer:

Example 2b

Simplify .

Communicative and Associative Properties

Product of Powers

Simplify.Answer:

Example 3

Simplify

Simplify.Answer:

Power of a Power

Simplify.

Power of a Power

Example 4

Geometry: Find the volume of a cube with a side length s = 5xyz

Simplify.Answer:

Volume Formula for volume of a cube

Power of a Product

Example 5

Simplify [(8g3h4)2]2(2gh5)4

Power of a Power

Power of a Product

Power of a Power

Commutative Property

Answer: Power of Powers

Summary & Homework

• Summary:– A monomial is a number, a variable, or a product

of a number and or one or more variables– To multiply two powers that have the same bass,

add exponents– To find a power of a power, multiply exponents– The power of a product is the product of powers

• Homework: – Pg. 413 16-40 even