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Lesson 1 KC1

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**Simplify Expressions with Multiplication**

A. Simplify (–2a3b)(–5ab4). (–2a3b)(–5ab4) = (–2 ● a ● a ● a ● b) ● (–5 ● a ● b ● b ● b ● b) Definition of exponents = –2(–5) ● a ● a ● a ● a ● b ● b ● b ● b ● b Commutative Property = 10a4b5 Definition of exponents Answer: 10a4b5 Lesson 1 Ex1

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**Simplify Expressions with Multiplication**

B. Simplify (3a5)(c–2)(–2a–4b3). (3a5)(c–2)(–2a–4b3) Definition of negative exponents Definition of exponents Lesson 1 Ex1

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**Simplify Expressions with Multiplication**

Cancel out common factors. Definition of exponents and fractions Answer: Lesson 1 Ex1

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**A. Simplify (–3x2y)(5x3y5). A. –15x5y6 B. –15x6y5 C. 15x5y6 D. A B C D**

Lesson 1 CYP1

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B. Simplify (4x–2)(xy–3). A. B. C. D. A B C D Lesson 1 CYP1

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Lesson 1 KC2

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Lesson 1 KC3

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**Simplify Expressions with Division**

Subtract exponents. Remember that a simplified expression cannot contain negative exponents. Answer: Lesson 1 Ex2

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A. x10 B. x21 C. x4 D. A B C D Lesson 1 CYP2

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Lesson 1 KC4

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**Simplify Expressions with Powers**

A. Simplify (–3c2d5)3. (–3c2d5)3 = (–3)3(c2)3(d5)3 Power of a power = –27c6d15 Simplify. Answer: –27c6d15 Lesson 1 Ex3

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**Simplify Expressions with Powers**

B. Power of a quotient Power of a product (–2)5 = –32 Answer: Lesson 1 Ex3

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A. Simplify (x3)5. A. x15 B. x8 C. x2 D. A B C D Lesson 1 CYP3

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B. Simplify A. B. C. D. A B C D Lesson 1 CYP3

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**Simplify Expressions Using Several Properties**

Method 1 Raise the numerator and the denominator to the fifth power before simplifying. Lesson 1 Ex4

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**Simplify Expressions Using Several Properties**

Answer: Lesson 1 Ex4

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**Simplify Expressions Using Several Properties**

Method 2 Simplify the fraction before raising to the fifth power. Lesson 1 Ex4

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**Simplify Expressions Using Several Properties**

Answer: Lesson 1 Ex4

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A. B. C. D. A B C D Lesson 1 CYP4

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**← number of red blood cells in sample **

BIOLOGY There are about 5 × 106 red blood cells in one milliliter of blood. A certain blood sample contains 8.32 × 106 red blood cells. About how many milliliters of blood are in the sample? Divide the number of red blood cells in the sample by the number of red blood cells in 1 milliliter of blood. ← number of red blood cells in sample ← number of red blood cells in 1 milliliter Answer: There are about 1.66 milliliters of blood in the sample. Lesson 1 Ex5

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**BIOLOGY A petri dish started with 3. 6 × 105 germs in it**

BIOLOGY A petri dish started with 3.6 × 105 germs in it. A half hour later, there are 7.2 × 107. How many times as great is the amount a half hour later? A. 2 B. 20 C. 2 × 102 D × 1013 A B C D Lesson 1 CYP5

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End of Lesson 1

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**A. Simplify (2a3 + 5a – 7) – (a3 – 3a + 2).**

Simplify Polynomials A. Simplify (2a3 + 5a – 7) – (a3 – 3a + 2). (2a3 + 5a – 7) – (a3 – 3a + 2) Distribute the –1. Group like terms. = a3 + 8a – 9 Combine like terms. Answer: a3 + 8a – 9 Lesson 2 Ex2

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**B. Simplify (4x2 – 9x + 3) + (–2x2 – 5x – 6).**

Simplify Polynomials B. Simplify (4x2 – 9x + 3) + (–2x2 – 5x – 6). (4x2 – 9x + 3) + (–2x2 – 5x – 6) Remove parentheses. Group like terms. = 2x2 – 14x – 3 Combine like terms. Answer: 2x2 – 14x – 3 Lesson 2 Ex2

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**A. Simplify (3x2 + 2x – 3) – (4x2 + x – 5).**

A. 7x2 + 3x – 8 B. –x2 + 3x – 8 C. –x2 + 3x + 2 D. –x2 + x + 2 A B C D Lesson 2 CYP2

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**B. Simplify (–3x2 – 4x + 1) – (4x2 + x – 5).**

A. 9x2 + 6x + 7 B. –7x2 – 5x + 6 C. 3x2 – 6x + 7 D. 3x2 – 2x + 6 A B C D Lesson 2 CYP2

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**Simplify Using the Distributive Property**

Find –y(4y2 + 2y – 3). –y(4y2 + 2y – 3) = –y(4y2) –y(2y) – y(–3) Distributive Property = –4y3 – 2y2 + 3y Multiply the monomials. Answer: –4y3 – 2y2 + 3y Lesson 2 Ex3

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**Find –x(2x3 – 2x + 5). A. –3x2 – 2x + 5 B. –4x4 – 3x2 – 6x**

C. –3x4 + 2x2 – 5x D. –3x4 – 2x3 + 5x A B C D Lesson 2 CYP3

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**Distributive Property**

Multiply Polynomials Find (a2 + 3a – 4)(a + 2). (a2 + 3a – 4)(a + 2) Distributive Property Distributive Property Multiply monomials. = a3 + 5a2 + 2a – 8 Combine like terms. Answer: a3 + 5a2 + 2a – 8 Lesson 2 Ex4

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**Animation: Multiply Polynomials**

Find (x2 + 3x – 2)(x + 4). A. x3 + 7x2 + 10x – 8 B. x2 + 4x + 2 C. x3 + 3x2 – 2x + 8 D. x3 + 7x2 + 14x – 8 A B C D Animation: Multiply Polynomials Lesson 2 CYP4

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End of Lesson 2

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