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Splash Screen Chapter 10 Lesson 10-6 (over Lesson 10-4) A. C B. . D. A. B. C. A B D (over Lesson 10-5) Find 3y 4(5y 2). Express using exponents. A. 15y 6 B. 15y 2 C. 8y 6 D. 8y 2 A. B. C. D. A B C D (over Lesson 10-5) Multiply 4(–3) ● 4(–4). Express using positive exponents. A. B. C. 16y 2 D. 16y 12 1. 2. 3. 4. A B C D (over Lesson 10-5) Multiply (–3x6yz2)(–2xy–3). Express using positive exponents. A. 6x7y–2z2 B. C. D. 1. 2. 3. 4. A B C D • Divide monomials. Standard 7NS2.3 Multiply, divide, and simplify rational numbers by using exponent rules. Standard 7AF2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents. Standard 7AF2.2 Multiply and divide monomials; extend the process of taking powers and extracting roots to monomials when the latter results in a monomial with an integer exponent. 35 33 = 32 129 5 12 = 124 Here’s your 1st math challenge of the day: 2116 5 21 = 2111 67 = 6 6 6 So let’s analyze what’s happening. When you divide monomials that have the same base: 35 2 3 = 33 129 5 12 = 124 2116 5 21 = 2111 You keep the base and subtract the exponents. Remember when we learned how to do this: Remember this and apply-4it to1your 3 = 4 nd 3 2 challenge of this We simply turned any base with a negative exponent into a fraction with a lesson! denominator of 1 and and the exponent becomes positive. 3-5 1 -8 3 = = 33 38 12-9 = 124 12-13 = 1 1213 Here’s your 2nd math challenge of the day: 21-6 1 -7 = 21 = 21 217 1 66 -1 = 6 = 7 6 6 When So let’s youanalyze divide what’s monomials happening. and get a negative exponent: 3-5 1 -8 = 3 = 8 3 3 3 12-9 = 4 12 12-13 = 1 1213 You create a fraction with a numerator of 1 & the base & the exponent become the denominator. The exponent changes to positive. Remember when we learned how to do this: Remember this and apply it to your -5 – (-6) = 1 rd 3 challenge of this When we subtract a negative (we call that a double negative), we lesson! change it to a positive then combine. 6-3 2 =6 -5 6 129 13 12 = 12-4 Here’s your 3rd math challenge of the day: X-11 -16 x = 5 x y-6 -1 = 1 Y = y-7 y When you divide monomials subtract a So let’s analyze what’sand happening. negative: -3 - (-5) = -3 + 5 = 2 6-3 = 62 6-5 -7 - (-6) = -7 + 6 = -1 y-7 1 = -6 y y You turn the double negative into a positive then combine. If you get a (+) exponent you’re done. If you get a (-) exponent, create a fraction to turn the exponent to a (+). Divide Powers Simplify Express using exponents. The common base is 6. Subtract the exponents. Simplify. Answer: 610 Divide Powers Simplify Express using exponents. The common base is a. Subtract the exponents. Simplify. Answer: a6 Use Negative Exponents The common base is 8. Subtract the exponents. Simplify. Subtract the exponents. Make the base & negative exponent into a denominator to make the exponent positive. Use Negative Exponents The common base is x. Subtract the exponents. Here you have a double negative. Remember the rule. The double negative makes the 1 a 1. Now combine them & simplify. Make the base & negative exponent into a denominator to make the exponent positive. Simplify Express using exponents. A. 34 B. 36 C. 38 D. 310 1. 2. 3. 4. A B C D Simplify Express using exponents. A. x6 B. x8 C. x 12 D. x14 A. B. C. D. A B C D Simplify . Express using positive exponents. A. B. C. 55 D. 511 1. 2. 3. 4. A B C D Simplify . Express using positive exponents. A. B. C. a 5 D. a13 A. B. C. D. A B C D Simplify . Express using positive exponents. A. B. C. 6b11 D. A. B. C. D. A B C D POPULATION The population of the state of Michigan is about 107. The population of Alger County, Michigan is about 104. How many times larger is the population of Michigan than the population of Alger County? A. 102 B. 103 C. 104 D. 105 A. B. C. D. A B C D