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

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6-1 Integer Exponents Warm Up Lesson Presentation Lesson Quiz
Holt McDougal Algebra 1 Holt Algebra 1

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

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

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

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

Base x Exponent Remember! 4

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.

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

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

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

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

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

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

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

Objective Multiply polynomials.

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

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.

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.

When multiplying powers with the same base, keep the base and add the exponents.
x2  x3 = x2+3 = x5 Remember!

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

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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