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Name ____________________________________________________________________________________ Date _______________________ MOD 15 - STUDY GUIDE You may use a four function calculator. Work with radicals and integer exponents I can create equivalent numerical expressions using the properties of integer exponents. 1) Simplify the expression 45 ∙ 42 a) Using exponents: b) Evaluate: 35 33 a) Using exponents: b) Evaluate: 3) Find the value of x to make the statement true. (𝑏 4 )𝑥 = 𝑏16 \ 2) Simplify the expression 4) What is the value of 5−3 ? Name: Grade 7acc Module 15 5) Choose all the expressions that are equivalent to 55 6) Use properties of exponents to find the value of x. 55 Hint: you want to make the left side equal to the right side. 44 ∙ 43 ∙ 4𝑥 = 410 42 7) Simplify the expression. (10 − 2)3 − 42 + (12 )3 Page 2 Name: Grade 7acc Module 15 8.EE.3 Learning Target: Express quantities using integer powers of 10. Using scientific notation, describe the relationship between quantities. 8.EE.4 Learning Target: Perform operations using scientific notation. Describe and interpret real-world situations using scientific notation. 8) Write in standard form. 1.09 × 106 6.21 × 100 8.52 × 10−3 7 × 10−5 9) Write in scientific notation. 93,000,000 1,637,000,000 0.000435 0.00103 27 × 102 25.7 × 104 13 × 10−2 4.5 × 10−3 Page 3 Name: 10) Grade 7acc Module 15 Write the numbers from smallest to largest. 3 × 103 , 4 × 102 , 3.2 × 10−3 , 4 × 10−3 2 × 105 , 3 × 104 , 2.3 × 10−5 , 1 × 105 11) Estimate the state populations as a single-digit integers times a power of 10. State 2012 population Estimated 2012 population California 38,041,430 4 × 107 Texas 26,059,203 New York 19,570,261 Florida 19,317,568 Illinois 12,875,255 12) Circle all of the measurements that would most likely be recorded in scientific notation. Distance between planets Mass of an electron in grams Distance from Chicago to New York in miles Weight of a suitcase in pounds Number of stars in the universe Ounces of milk in a glass Number of people in the world Gallons of water in Lake Michigan Page 4 Name: 13) 14) Grade 7acc Module 15 Choose the most appropriate unit of measurement to use. your age seconds years distance from California to New York inches feet weight of an atom milligrams grams decades miles kilograms Evaluate the expression. Write in scientific notation. (𝟗 × 𝟏𝟎𝟔 ) + (𝟕 × 𝟏𝟎𝟔 ) (𝟗 × 𝟏𝟎𝟔 ) − (𝟕 × 𝟏𝟎𝟔 ) (𝟏. 𝟐 × 𝟏𝟎𝟓 ) + (𝟑. 𝟕 × 𝟏𝟎𝟑 ) (𝟗. 𝟖 × 𝟏𝟎𝟒 ) − (𝟏 × 𝟏𝟎𝟑 ) Page 5 Name: 15) Grade 7acc Module 15 Evaluate the expression. Write in scientific notation. (𝟔 × 𝟏𝟎−𝟐 )(𝟑 × 𝟏𝟎𝟒 ) (𝟐. 𝟏 × 𝟏𝟎𝟔 )(𝟑 × 𝟏𝟎−𝟏𝟎 ) (𝟗 × 𝟏𝟎𝟖 ) (𝟐 × 𝟏𝟎𝟒 ) (𝟑. 𝟔 × 𝟏𝟎𝟒 ) (𝟔 × 𝟏𝟎−𝟓 ) (𝟐 × 𝟏𝟎𝟏𝟓 ) (𝟖 × 𝟏𝟎𝟕 ) (𝟗 × 𝟏𝟎−𝟑 ) (𝟑 × 𝟏𝟎−𝟕 ) Page 6 Name: Grade 7acc Module 15 A lightning bug weighs about 𝟏. 𝟓 × 𝟏𝟎−𝟒 kg. A flea weighs about 𝟑 × 𝟏𝟎−𝟒 kg. A horse weighs about 𝟗 × 𝟏𝟎𝟐 kg. 16) How many times larger is a lightning bug than a flea? (Write in standard notation.) How many times larger is a horse than a flea? (Write in standard notation.) How many kilograms would 2 million lightning bugs weigh? (Write in scientific notation.) How many kilograms would 4 horses weigh? (Write in scientific notation.) Page 7