Multiplying and Dividing Monomials

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Multiplying and Dividing Monomials
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Objectives

• Understand the concept of a monomial
• Use properties of exponents to simplify
  expressions

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Monomial

• An expression that is either

• a constant

• a variable

• a product of a constant and 1 or
• more variables

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Multiply

• (a3b4)(a5b2)

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

• (5a4b3)(2a6b5)

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Multiply

• (5a4b3)(2a6b5)

Multiply the coefficients
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Multiply

• (5a4b3)(2a6b5)

10(a4b3)(a6b5)
Multiply the coefficients
Group like bases
10(a4a6)(b3b5)
Answer 10 a10b8
When multiplying, add the exponents.
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Try This!

• 1. (a2b3)(a9b)

Answer a11b4
2. (3a12b4)(-5ab2)(a3b8)
Answer -15a16b14
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Divide

• a7b5
• a4b

Group like bases
When dividing, subtract the exponents
(a7 - 4)(b5 - 1)
Answer a3b4
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Divide

• -30x3y4
• -5xy3

Divide the coefficients. Group like bases
(x3 - 1)(y4 - 3)
Answer 6x2y
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Divide

• 2m5n4
• -3m4n2

Divide the coefficients. Group like bases
(m5 - 4)(n4 - 2)
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Try This!

• 1. m8n5
• m4n2

(m8 - 4)(n5 - 2)
(x10 - 9)(y7 - 2)
Answer m4n3
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Power of a Product
(ab)3

• (ab)2

(ab)(ab)(ab)
(ab)(ab)
(aaa)(bbb)
(aa)(bb)
a3b3
a2b2
Rule 4 (xy)n xnyn
Multipy the exponent outside the () times
each exponent inside the ().
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Power of a Product
(4m11n20)2

• (a9b5)3

(41m11n20)2
(a93)(b53)
(412)(m112)(n202)
Answer a27b15
Answer 16m22n40
Rule 4 (xy)n xnyn
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4

• x
• y

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Try This!
2. (4xy5z2)4

• 1. (2a4)3

(41x1y5z2)4
(21a4)3
(213)(a43)
(414)(x14)(y54)(z24)
Answer 8a12
Answer 256x4y20z8
Rule 4 (xy)n xnyn