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Lesson 7.3: Define and Use Zero and Negative Exponents Essential Question: How do you evaluate exponential expressions involving zero and negative exponents? Common Core CC.9-12.A.SSE.3c Use the properties of exponents to transform expressions for exponential functions. 1-14-14 Warm-up: Check your homework !

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Definition of Zero and Negative Exponents Algebra Example

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Use definition of zero and negative exponents EXAMPLE 1 a. 3 – 2 Definition of negative exponents 1 9 = Evaluate exponent. b. (–7) 0 Definition of zero exponent 1 3232 = = 1

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Use definition of zero and negative exponents EXAMPLE 1 = 25 Simplify by multiplying numerator and denominator by 25. d. 0 – 5 a – n is defined only for a nonzero number a. 1 0 5 (Undefined) = = 1 5 1 2 5 –2 1 c. Definition of negative exponents 1 25 1 = Evaluate exponent.

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GUIDED PRACTICE for Example 1 Evaluate the expression. 0 2 3 1. = 1 1 64 = 2. (–8) – 2 1 2 3. –3 = 8 4. (–1 ) 0 = 1

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Properties of Exponents Product of powers propertyProduct of powers property Power of a power propertyPower of a power property Power of a product propertyPower of a product property Quotient of powers propertyQuotient of powers property Power of a quotient propertyPower of a quotient property Let a and b be real numbers, and let m and n be integers.

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EXAMPLE 2 Evaluate exponential expressions a. 6 – 4 6 4 Product of a power property = 6 0 Add exponents. = 1 Definition of zero exponent = 6 – 4 + 4

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EXAMPLE 2 Evaluate exponential expressions 1 256 = Evaluate power. c. 1 3 – 4 Definition of negative exponents Evaluate power. = 81 = 3 4 Power of a power property = 4 – 4 Multiply exponents. Definition of negative exponents b. (4 – 2 ) 2 1 4 = 4 = 4 – 2 ∙ 2

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EXAMPLE 2 Evaluate exponential expressions 1 125 = Evaluate power. d. 5 – 1 5252 Quotient of powers property = 5 – 3 Subtract exponents. 1 5353 = Definition of negative exponents = 5 – 1 – 2

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GUIDED PRACTICE for Example 2 5. 1 4 – 3 = 64 Evaluate the expression. 6. (5 – 3 ) – 1 = 125 7. (– 3 ) (– 3 ) – 5 5 = 1 8. 6 – 2 6262 1 1296 =

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EXAMPLE 3 Use properties of exponents Simplify the expression. Write your answer using only positive exponents. a. (2xy –5 ) 3 = 2 3 x 3 (y –5 ) 3 = 8 x 3 y –15 = y 15 8x38x3 Power of a product property Power of a power property Definition of negative exponents

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EXAMPLE 3 Use properties of exponents y5y5 (2x) 2 (–4x 2 y 2 ) = (2x) –2 y 5 –4x 2 y 2 b. y5y5 (4x) 2 (–4x 2 y 2 ) = y5y5 –16x 4 y 2 = y3y3 16x 4 – = Power of a product property Definition of negative exponents Product of powers property Quotient of powers property

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EXAMPLE 4 Standardized Test Practice The order of magnitude of the mass of a polyphemus moth larva when it hatches is 10 -3 gram. During the first 56 days of its life, the moth larva can eat about 10 5 times its own mass in food. About how many grams of food can the moth larva eat during its first 56 days ? A 10 –15 gram B 0.00000001 gram C 100 grams D 10,000,000 grams

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SOLUTION EXAMPLE 4 Standardized Test Practice To find the amount of food the moth larva can eat in the first 56 days of its life, multiply its original mass, 10 – 3, by 10 5. 10 5 10 –3 The moth larva can eat about 100 grams of food in the first 56 days of its life. ANSWER The correct answer is C. A B C D = 10 2 = 100 = 10 5 + (–3)

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GUIDED PRACTICE for Examples 3 and 4 9x3y9x3y 3xy – 3 9. Simplify the expression. Write your answer using only positive exponents. 1 3x2y43x2y4 ANSWER 10. SCIENCE The order of magnitude of the mass of a proton is 10 4 times greater than the order of magnitude of the mass of an electron, which is 10 –27 gram. Find the order of magnitude of the mass of a proton. ANSWER 10 –23 g

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Classwork/Homework 7.3 Exercises 2-54 even Pages 452 - 453

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