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