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Zero and Negative Exponents

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Presentation on theme: "Zero and Negative Exponents"— Presentation transcript:

1 Zero and Negative Exponents
ALGEBRA 1 LESSON 1-7 (For help, go to Lessons 1-2 and 1-6.) Simplify each expression. 1 42  22 4. (–3)3 5. –  12 Evaluate each expression for a = 2, b = –1, c = 0.5. a 2a bc c ab bc 1-7

2 Zero and Negative Exponents
ALGEBRA 1 LESSON 1-7 1. 23 = 2 • 2 • 2 = 8 = = 3. 42  22 = = = = 4 4. (–3)3 = (–3)(–3)(–3) = 9(–3) = –27 5. –33 = –(3 • 3 • 3) = –(9 • 3) = –27 6. 62  12 = 36  12 = 3 for a = 2: = for b = –1, c = 0.5: = –1 for a = 2, b = –1, c = 0.5: = = 4 Solutions 1 42 1 4 • 4 1 16 42 22 4 • 4 2 • 2 16 4 a 2a 2 2 • 2 1 2 bc c –1 • 0.5 0.5 ab bc 2 • (–1) (–1) • 0.5 2 0.5 1-7

3 Zero and Negative Exponents
ALGEBRA 1 LESSON 1-7 Simplify. = Use the definition of negative exponent. 1 32 a. 3–2 Simplify. 1 9 = b. (–22.4)0 Use the definition of zero as an exponent. = 1 1-7

4 Zero and Negative Exponents
ALGEBRA 1 LESSON 1-7 Simplify 1 x –3 a. 3ab –2 1 b2 Use the definition of negative exponent. = 3a b. Rewrite using a division symbol. = 1  x –3 = 1  1 x 3 Use the definition of negative exponent. Simplify. 3a b 2 = = 1 • x 3 Multiply by the reciprocal of , which is x 3. 1 x3 = x 3 Identity Property of Multiplication 1-7

5 Zero and Negative Exponents
ALGEBRA 1 LESSON 1-7 Evaluate 4x 2y –3 for x = 3 and y = –2. Method 1: Write with positive exponents first. 4x 2y –3 = Use the definition of negative exponent. 4x 2 y 3 Substitute 3 for x and –2 for y. 4(3)2 (–2)3 = 36 –8 –4 1 2 = Simplify. 1-7

6 Zero and Negative Exponents
ALGEBRA 1 LESSON 1-7 (continued) Method 2: Substitute first. 4x 2y –3 = 4(3)2(–2)–3 Substitute 3 for x and –2 for y. 4(3)2 (–2)3 = Use the definition of negative exponent. 36 –8 –4 1 2 = Simplify. 1-7

7 Zero and Negative Exponents
ALGEBRA 1 LESSON 1-7 In the lab, the population of a certain bacteria doubles every month. The expression 3000 • 2m models a population of 3000 bacteria after m months of growth. Evaluate the expression for m = 0 and m = –2. Describe what the value of the expression represents in each situation. a. Evaluate the expression for m = 0. 3000 • 2m = 3000 • 20   Substitute 0 for m. = 3000 • 1 Simplify. = 3000 When m = 0, the value of the expression is This represents the initial population of the bacteria. This makes sense because when m = 0, no time has passed. 1-7

8 Zero and Negative Exponents
ALGEBRA 1 LESSON 1-7 (continued) b. Evaluate the expression for m = –2. 3000 • 2m = 3000 • 2–2 Substitute –2 for m. = 3000 • Simplify. = 750 1 4 When m = –2, the value of the expression is 750. This represents the 750 bacteria in the population 2 months before the present population of 3000 bacteria. 1-7

9 Zero and Negative Exponents
ALGEBRA 1 LESSON 1-7 Simplify each expression. 1. 3–4 2. (–6)0 3. –2a0b–2 4. • • 3–2 1 81 1 2 b2 k m–3 km3 8000 500 1-7


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