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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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Division with Exponents & Negative and Zero Exponents.

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