2 Warm UpEvaluate each expression for the given values of the variables.1. x3y2 for x = –1 and y = 10for x = 4 and y = (–7)Write each number as a power of the given base.–1003. 64; base 4434. –27; base (–3)(–3)3
3 Objectives Evaluate expressions containing zero and integer exponents. Simplify expressions containing zero and integer exponents.
4 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.PowerValue5554535251505–15–23125625125255 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.
8 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.
9 2–4 is read “2 to the negative fourth power.” Reading Math
10 Example 1: ApplicationOne cup is 2–4 gallons. Simplify this expression.gal is equal to
11 Check It Out! Example 1A sand fly may have a wingspan up to 5–3 m. Simplify this expression.5-3 m is equal to
12 Example 2: Zero and Negative Exponents Simplify.A. 4–3B. 70Any nonzero number raised to the zero power is 1.7º = 1C. (–5)–4D. –5–4
13 In (–3)–4, the base is negative because the negative sign is inside the parentheses. In –3–4 the base (3) is positive.Caution
17 To multiply monomials and polynomials, you will use some of the properties of exponents that you learned earlier in this chapter.
18 Example 1: Multiplying Monomials A. (6y3)(3y5)(6y3)(3y5)Group factors with like bases together.(6 3)(y3 y5)18y8Multiply.B. (3mn2) (9m2n)(3mn2)(9m2n)Group factors with like bases together.(3 9)(m m2)(n2 n)27m3n3Multiply.
19 Example 1C: Multiplying Monomials 4s2 t2(st) (-12 s t2)()æçè-21124tsö÷øGroup factors with like bases together.()•æöçè21−124ts÷ø••Multiply.
20 When multiplying powers with the same base, keep the base and add the exponents. x2 x3 = x2+3 = x5Remember!
21 Group factors with like bases together. (3x3)(6x2) Check It Out! Example 1Multiply.a. (3x3)(6x2)Group factors with like bases together.(3x3)(6x2)(3 6)(x3 x2)Multiply.18x5b. (2r2t)(5t3)Group factors with like bases together.(2r2t)(5t3)(2 5)(r2)(t3 t)Multiply.10r2t4
22 Check It Out! Example 1 Continued Multiply.æ1ö()()c.x y212x z3245ç÷y zè3ø()æçè4521123xzyö÷øGroup factors with like bases together.()æçè3245112zx xy yö÷ø••Multiply.••754xyz