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**6-1 Integer Exponents Warm Up Lesson Presentation Lesson Quiz**

Holt McDougal Algebra 1 Holt Algebra 1

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Warm Up Evaluate each expression for the given values of the variables. 1. x3y2 for x = –1 and y = 10 for x = 4 and y = (–7) Write each number as a power of the given base. –100 3. 64; base 4 43 4. –27; base (–3) (–3)3

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**Objectives Evaluate expressions containing zero and integer exponents.**

Simplify expressions containing zero and integer exponents.

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**You have seen positive exponents**

You have seen positive exponents. Recall that to simplify 32, use 3 as a factor 2 times: 32 = 3 3 = 9. But what does it mean for an exponent to be negative or 0? You can use a table and look for a pattern to figure it out. Power Value 55 54 53 52 51 50 5–1 5–2 3125 625 125 25 5 5 5 5 5

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When the exponent decreases by one, the value of the power is divided by 5. Continue the pattern of dividing by 5.

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Base x Exponent Remember! 4

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**Notice the phrase “nonzero number” in the previous table**

Notice the phrase “nonzero number” in the previous table. This is because 00 and 0 raised to a negative power are both undefined. For example, if you use the pattern given above the table with a base of 0 instead of 5, you would get 0º = . Also 0–6 would be = . Since division by 0 is undefined, neither value exists.

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**2–4 is read “2 to the negative fourth power.”**

Reading Math

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Example 1: Application One cup is 2–4 gallons. Simplify this expression. gal is equal to

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Check It Out! Example 1 A sand fly may have a wingspan up to 5–3 m. Simplify this expression. 5-3 m is equal to

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**Example 2: Zero and Negative Exponents**

Simplify. A. 4–3 B. 70 Any nonzero number raised to the zero power is 1. 7º = 1 C. (–5)–4 D. –5–4

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In (–3)–4, the base is negative because the negative sign is inside the parentheses. In –3–4 the base (3) is positive. Caution

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**Multiplying Polynomials**

6-5 Multiplying Polynomials Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1 Holt Algebra 1

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Warm Up Evaluate. 1. 32 3. 102 Simplify. 4. 23 24 6. (53)2 9 2. 24 16 100 27 5. y5 y4 y9 56 7. (x2)4 x8 8. –4(x – 7) –4x + 28

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Objective Multiply polynomials.

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To multiply monomials and polynomials, you will use some of the properties of exponents that you learned earlier in this chapter.

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**Example 1: Multiplying Monomials**

A. (6y3)(3y5) (6y3)(3y5) Group factors with like bases together. (6 3)(y3 y5) 18y8 Multiply. B. (3mn2) (9m2n) (3mn2)(9m2n) Group factors with like bases together. (3 9)(m m2)(n2 n) 27m3n3 Multiply.

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**Example 1C: Multiplying Monomials**

4 s2 t2 (st) (-12 s t2) ( ) æ ç è - 2 1 12 4 t s ö ÷ ø Group factors with like bases together. ( ) • æ ö ç è 2 1 −12 4 t s ÷ ø • • Multiply.

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**When multiplying powers with the same base, keep the base and add the exponents.**

x2 x3 = x2+3 = x5 Remember!

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**Group factors with like bases together. (3x3)(6x2)**

Check It Out! Example 1 Multiply. a. (3x3)(6x2) Group factors with like bases together. (3x3)(6x2) (3 6)(x3 x2) Multiply. 18x5 b. (2r2t)(5t3) Group factors with like bases together. (2r2t)(5t3) (2 5)(r2)(t3 t) Multiply. 10r2t4

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**Check It Out! Example 1 Continued**

Multiply. æ 1 ö ( ) ( ) c. x y 2 12 x z 3 2 4 5 ç ÷ y z è 3 ø ( ) æ ç è 4 5 2 1 12 3 x z y ö ÷ ø Group factors with like bases together. ( ) æ ç è 3 2 4 5 1 12 z x x y y ö ÷ ø • • Multiply. • • 7 5 4 x y z

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